Very Feasible
The entire premise of SpaceX is that launch costs can be reduced by 10-100x by building reusable rockets (believe it or not, the fuel is actually a minor cost of rocket launches). We do not have artificial gravity space stations yet, but there are no obvious physical barriers to doing so (mostly engineering and cost barriers).
Why
The problem with jets is that we have a very mature set of weapons systems designed to defeat them, from SAMs to interceptor aircraft. And transports are almost never designed to be very fast, because they are almost always used after air superiority has been achieved. Rather, they are designed to be flexible, so they can deliver troops to inhospitable terrain (c.f. Osprey, Chinook, etc.).
Right now, the only weapons systems we have for anti-space defense are ICBM interceptor batteries, which are mostly untested and probably unreliable. Most tests of such systems fail to reach the target or fail to destroy the target. An orbital delivery vehicle would presumably be armored if there were credible defenses which could attack it. Combined with thrusters for evasive maneuvers, such a vehicle should be extremely hard to hit.
Where
If you look at the placement of AA defenses, they are situated on the borders of countries and around high-value targets. Space offers a border with the entire surface area of the country. You can't blanket all of China or Russia with AA batteries. But clearly, an orbital drop would be a good choice away from conventional AA defenses.
Who
Obviously, you wouldn't use an infantry drop to shoot a thug or blow up a building. You would use it for target extraction or minimal collateral damage or to reach targets which are hardened against other kinds of attacks (like deep underground facilities).
Logistics
In addition to having multiple space barracks, you could rotate your marines/Spec Ops teams so they don't spend too much time in space (where they are exposed to a lot more radiation than on the ground), say, every 3 months. And obviously, you would not just put average grunts in space. You would want highly trained fighters, at the least, and possibly your best troops, if that becomes the most effective way to deliver them to the battlefield in the future.
Limitations
Although an orbital drop lacks subtlety, what it gains is logistical speed. It would be easy to drop into an area which does not have ready defenders, and gain a significant time advantage against a less protected target. Of course, dropping into an area with a lot of defenders is probably a very poor strategy. Even then, the battlefield can be prepped via kinetic bombardment (though defeating air forces would be harder from space, unless you also have energy weapons).
If you consider how long it took to get F-16s on station on 9/11, it is easy to see how soft the interior of most countries is. That was just a few jets. Imagine trying to mobilize a squadron against an orbital drop. It would be very difficult to get them prepped and ready in time to meet the space marines, even if you knew where they were going to land 30 minutes in advance. And if they were snake eaters, then they could land well away from the intended target and infiltrate the countryside, making it extremely difficult to find them.
My guess is that space will be militarized with marines just as soon as countries can afford it and have a good reason to do so.