No, it is not.
From the way you're approaching the situation I think you're not considering that the world in the 1500's had a radically different view on life and inter-nation relationships.
In this day and age borders in Europe are pretty stable (as in European nations no longer go to war with one another over land in Europe), but that was not the case going back as recently as the Second World War. (The whole Crimean situation is not being taken under consideration right now).
Political Landscape
Europe was divided into many states, and city states, some of which held their allegiance to a monarch only by a very frayed string. The concept of a "nation" did not really exist as it does today.
Italy, for example, was not one nation, but composed of many city states, each of which was populated with Italians, and each of which slaughtered the other at the slightest opportunity for gain.
Furthermore, a lot of ruling families were related by marriage, and/or had long-lasting feuds with one another.
The reason that you'll find so many castles in Europe is because they were needed, and badly. War, at the local or continental level, was constant, with nobles trying to capture neighboring city states, maneuvering politically and militarily to annex the lands of a rival, or simply avenging an insult.
It was 100% normal for a city state to change leadership several times in a decade. The show "The Borgia" (the European one, not the North-American one) really gives great insight into how fluid alliances, borders, and motivations were at that time.
It was all quite chaotic, with monarchs fighting one another, then ganging up on a third rival only to fight each other once more.
Culture
The value of human life is always relative. In the West we like to think that each and every one of us is a precious individual with the right to live a free and happy life. Our hypocrisy is easily exposed when we cause thousands of civilian casualties in countries like Iraq, and find that we don't really care that those people die. It's in the media, we ooh and aah for a few days, then get sucked into choosing our next smart-phone, etc.
Well, in the 1500's the value of a peasant's life was somewhere in the negatives, and the peasant knew it. You look at a noble the wrong way and he WILL skewer you, with little to no consequences for doing so.
In that day and age personal insults were a perfectly legitimate reason to kill someone (in a duel, for example). However, power structures were also very much based on family relationships. If you duel and kill the wrong youngster in the local tavern, you may soon find out that he was the cousin of some high-lord in a neighboring city-state, who will now use this incident as an excuse to launch a campaign against your own city.
Standing Army
First of all, any country with no standing army is inviting invasion. Some diplomatic maneuvering may save you for a while, but sooner or later (with my bet being on sooner) your neighbors are going to start stripping pieces of land away from you.
Furthermore, at that time nations did not necessarily have a national army in the sense that we do today. Individual lords and other nobles would be entitled (or even required by law) to have a certain number of infantry and cavalry under their command. Having too few, or too many was seen either as a weakness, or as a provocation respectively.
Conflict
The fact is that at that point in history a rivalry between two local noblemen over who's workers gets to cut logs in which forest could easily result in an armed clash before the matter ends up being settled in front of the king. In fact, by the time the officials are informed, the king summons both nobles over, they arrive, a decision is made, and they both go home and implement the ruling (or not), months or even a year may have passed.
Example: A forest straddles the territory between two baron's lands. Some very fine trees grow in that forest, which are perfect for construction projects which both lords are heavily invested in.
Barron A's woodcutters venture deep into said forest, close to Barron B's land in order to cut down the finest trees (into "contested" territory). They commence operations and are at it for a few days before Barron B's woodcutters run into them. The two groups come to blows over who has the right to cut down those trees.
Barron B is outraged & sends his captain and several men-at-arms to evict the "invading" woodcutters. In the mean time, Barron A sends his own troops to protect his operation. The two groups meet in the clearing and face off. Barron A's troops claim that the other group is trespassing, and vice-versa. Heavy words are spoken, and both captains back off, but only just. Barron B's captain, however, launches a surprise attack in the night. Archers, with fire-arrows kill several of Barron A's troops and woodcutters, and they destroy much of their equipment.
Barron A now sends a complaint to the King, as does Barron B. However, not wanting to be judged as weak, he also sends troops to torch some of Barron B's watch-towers, as well as seizing cattle and sheep worth "the price of what we lost".
The conflict keeps escalating, to the point that when the King finally steps in some weeks later one Barron's castle may already be besieged by the other.
Agriculture & Food
You're dealing with a time in history when food shortages, and starvation were not unusual. In the winter, with lots of snow on the ground (the Earth was experiencing a global cooling event in the 1400-1600's), some communities could be isolated until the snow melted. It was not entirely unusual for most of a village to have (mostly) starved to death during the winter months, and only have this be discovered in the spring.
Here's some facts:
There were no fridges, no canning, and no great ways of storing food.
If you slaughter an animal, you have to either salt it, smoke it, or just plain eat it. Even if you do try to preserve the meat it will still most likely go bad in the summer, or simply get eaten/spoiled by rodents, or other pests.
Transporting food is not a trivial task
Transporting food in the summer months is not a good ideas as it is almost guaranteed to go bad on the road. Conversely, in the winter it's very difficult to move around, and freezing to death on the road was not unheard of.
Not having food on hand is a huge vulnerability
Anyone wishing to invade your land would first cut off your food supply. By relying on imports (which is insanely unrealistic for that time period anyway) you're simply making it incredibly easy for them to starve you into surrender.
Art & Culture
Having a standing army, feeding your population, attracting artists, and pursuing scientific knowledge are not mutually exclusive in the least.
But be realistic about the people you're dealing with at that time in history. The vast majority of people (even today) have little to no culture, never go to an art gallery, don't listen to classical music, etc. They come home, crack open a bottle of beer, and sit down to watch their favorite sport or show for the rest of the night.
The common peasant back then was no different: they didn't care about the latest, flashiest painting hanging up in the King's parlor, they just wanted to make a living and survive the next winter. A drought impacts them. A new tax impacts them. The latest poem that the King enjoyed over drinks with his buddies is of no relevance to them.
However, try telling them that they can't farm anymore, because they are now expected to write poetry themselves. Food will be provided, in varying quantities, as available, and their only concern is lounging around and creating "Art". That's a great way to sink a nation if I've ever heard one.
City-States
There's a reason why the Renaissance took place in the city-states of Italy. Because the political landscape allowed rich cities to focus spend money on artists and other "frivolous" pursuits while having enough gold on hand to hire as many mercenaries as necessary to keep them safe. Even then the many nobles still had their own armies and fought not only neighboring cities, but also each other on a regular basis.
However, since the scope of each monarch was more limited, and their coffers quite full, they were able to much more easily allow a passion for arts and the pursuit of knowledge to grow.
Gearing an entire kingdom (the size of Switzerland no less) to do the same is not possible at that point in time. People need to be fed, and protected, not only from outside threats, but each other as well.
Furthermore, at this point in time it's quite common for a noble to pursue a higher title by murdering his betters, and monarchs were constantly being deposed. A king would be quite foolish to disband his own troops and trust purely in the obedience of his nobles, and the generosity of his neighbors, not only to not invade him, but feed his people.
