No need to get out of the calculator and it's not the only system in play that isn't linear.
And we can always add a system in play to say how much administrative capacity you would need to reduce the current administrative inefficiency one level.
If the formula has this form, it is also to avoid an exponential growth of penalties to allow big empires to exist, even if they will suffer big penalties and will need a large bureaucracy to avoid collapsing on themselves.
Since Stellaris can house large empires, an exponentially growing system can quickly become problematic.
For example, with your "idea" of double the previous pop, that makes: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, and I don't even have added the addition of the pops.
Even doing with x1.01 instead of x2, the 500th pop is 144.77 and the 600th is 391.58. I avoid cumulating. XD
Obviously you have to factor in the modifiers, but yeah, it ends up exploding "pretty quickly".
For example, in my example at 2000 empire sprawl (with equivalent administrative capacity), we are at level 8 of administrative inefficiency, at 10,000, we are at level 13 "only" (13,68). Certainly, at this level, the empire would already collapse no doubt. And it would undoubtedly be difficult to have an administration efficient enough to go down to at least level 10 (but that would depend on the impact of technologies, traditions and other modifiers), at this level (and before), it would undoubtedly be essential to have dependencies to remain viable.
It is not a "loophole", I speak about it precisely so that this loophole does not exist by creating a system which prevents this abuse. Note that currently you can well activate massive bureaucrats to unlock technologies and traditions and then deactivate them. This flaw already exists today.