As I've said elsewhere, the main issue with trying to move these assault armies around is that the ships are actually too small and not near numerous enough. Any given developed world should be able to comfortably support armies numbering in the millions, with all of the associated mechanized equipment and aero-fighter support. How many army units would represent that? A million human-equivalent troops (infantry) might be 50-100 US Army divisions (10-20K), 25-50 corps (20-40K), or (at most) 12-13 field armies (80K min each).
How big are each of the combat ship classes shown in Stellaris? Corvettes have the smallest basic combat frame, capable of mounting just three Small weapons - I'm estimating that the space required for each of those weapons emplacements is maybe 1,000 cubic meters. Times three is about 3,000 cubic meters or just enough room to somehow cram just the bodies (no equipment, shuttles, life support, living space, etc.) of about 750 human-equivalents. If your starting point is a 15K infantry division, you would need 20 Corvettes with no space weapons (and no defenses, assuming even THAT is enough to get in the things I left out before) just to get you that small amount. Based on the doubling in size per class, Destroyers would handle it in 10 ships, Cruisers in 5, and Battleships in 2-3. Again, no fleet weapons or defenses, just 15K troops.
Take on a lightly developed world, multiply that by at least 4 for every field army you need - a very modest assault force of 5 standard armies might be 2 corps each with 2 divisions each, or 300K infantry troops. That's the equivalent of 400 Corvettes, 200 Destroyers, 100 Cruisers, or 50 Battleships, all of which are only carrying armies.
Oh, I know, you could say that you're somehow cramming in some troops into every single ship without needing to take away space combat capability. How many would that be exactly? A few hundred per Corvette and multiplied up the line? Say 250 base without having to do anything else. Now do the math to get to the numbers above. Let me know when you get to the fleet hard cap. For 5 armies.
If you can ramp up your transport ships into the same base configuration as say a Colony Ship (which has its own size inadequacy issues - one whole POP inside of 1 ship, HA!), that might be big enough to convey a single division. Multiply by 4 to get each army, and then multiply by the number of armies needed. The numbers start to get a little silly, but they're really close to what you're faced with if you want ANY minimal level of realism, even in a sci-fi/psionic/extra-dimensional universe.
If you want to work with any of the numbers I've put up above, go ahead and recalculate - please show your work.
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