I'm pretty sure the whole point of the Empire Sprawl penalty is to keep big empires on par with small empires in certain areas. It shouldn't be thought of as a penalty, more like a necessary balancing mechanism that is there because the game treats research and unity the same as other resources, but doesn't want to see them grow linearly with the size of your empire.
The only reason admin capacity is a thing is because it fills a hole that was left when the core sector limit became obsolete. It works, but it's really not necessary in my opinion.
Admin Cap is actually a great mechanic. The problem is, the weights are way off. Defining size by economic potential makes sense because that's what the game needs to take into account, not some arbitrary property. But then one measly ecumonopolis district for 1 admin cap can support production equivalent of 20-30 admin cap worth of star systems.