"Prohibitively expensive" is how wars of invasion work. War is an intensely materiel-dependent operation, so discarding drop pods for rapid insertion seems like a weird thing to be pinching pennies about.

Ahw, you accepted it so quick!

@Mermaker It opened me up to more creative approaches. I might accept a different answer if a better one shows up though :P

I gave my 2¢ on the topic, too. Hopefully useful!

why would they use the same system for completely different atmospheres?

@John mass production. there are too many planets to make a custom drop pod for each invasion.

@alkahest custom no, 1 from several modular options almost certainly.

If you want to get your dropship back into orbit then you're going to need a massive and vulnerable rocket filled with explosive fuel - just ditching the dropship would probably be the least prohibitively expensive option, considering the alternative.

@N.Virgo: If the mothership can do the de-orbit burn then something like a fully fueled Blue Origin New Sheperd or an X-15 rocket plane is enough to get back up above atmosphere.

@AlexP Post your own answer with that solution. Just a heads up tho: the Falcon 9 first stage needs to deal with a suborbital speed of 2 km/s, from about 80 km of suborbital altitude, and no payload. Coming down from orbital altitude — 320 km, or more — and orbital speeds — 4 km/s, or more — with a full complement of troops and their equipment, is something different entirely than what the Falcon 9 first stage does. At a minimum, we are talking about 20 times the amount of energy to dissipate.

@Michael you still need to reach orbital speeds to dock with the mothership though. Although maybe the mothership could grab it with a skyhook once it gets above the atmosphere - it's not beyond the bounds of possibility. There would still be major challenges though because a New Shepard sized rocket is still vulnerable and packed with explosive fuel, and couldn't be armoured without making it much heavier, hence needing to be much bigger. It would itself have to be de-orbited along with the drop ship and survive the landing.

@jdunlop Have you considered the better question of how the soldiers, and whatever drops them, gets back into orbit? It costs a lot more energy to get those things back up than it does to get them down. And if they're not going to come back up, what exactly is the problem with a one time use dropship?

@Mathaddict i'm going to ask a separate question for that, this question's foundation isn't strong enough.

@Mathaddict If you're going to drop a soldier on 4 different worlds, at some point, you're going to need to lift 4 drop pods to the mothership. Whether you're lifting the same one 4 times or lifting 4 different drop pods to the mothership before it leaves Earth, you're paying the same fuel costs (+/- differences in atmosphere and gravity, which could increase or decrease fuel costs). The question is whether it costs more mass to have a single drop pod capable of reorbiting or 4 drop pods that aren't, because the mothership also needs to carry enough fuel to move the drop pods between worlds

IMO the question attacks the wrong problem - although the right problem might end up off topic. You've given your characters (including background characters like military planners) magic and are asking them to solve a problem in a way that involves using the magic. In this case, the magic is the Hyperdrive and the problem is getting men onto planets.

The capabilities and constraints of the tool are going to dictate the shape of the solution - so the question becomes either 'my hyperdrive has such and such capabilities and constraints, how do we solve the problem?' or 'my solution is such and such, what capabilities and constraints must the hyperdrive have for that to make sense?'