It might only take a couple of dozen crew to fly a Miranda in ideal conditions - but it could still take the full 200 to 400 crew to operate her in battle.
I would honestly be surprised if it took even nearly that many - why would a ship like that, presumably fitted out with reasonably modern systems, need a far larger crew than the comparable Defiant class ships?
Starfleet presumably has a far easier time churning out little cruisers than it has churning out its highly skilled crews. I imagine best use of personnel would make the allocation of 400 crew to a small combatant of limited capabilities in wartime unwise. Installing automated systems makes a lot more sense.
Warships in the real world have large crews simply because large scale automation of any systems is not really a reality in our time. That said the Royal Navy's new Carriers and Destroyers have smaller crews than ever before.
It seems odd to have massive ships like the Galaxy class with a mere 1000 personnel, maybe only 850 of these are crew! It would however be even more odd to stick 200 to 400 personnel on a (still huge) ship a fraction of its size?