Anyway, I've been giving this a lot of thought and reading some other discussions on this topic on these forums and have came to a couple conclusions I think will work for me and let me have a more balanced game next time through.
First, so far I'm just playing with what I get. I don't see myself wanting to do the hiring/firing route and only take soldiers with good starting stats. Once I get more money and multiple bases, I might throw the shit soldiers as base defenders at the South Pole, but no pink slips. Only way out is in a body bag.
Then...
Option 1: Leave psi on, don't require LOS, but have a self-imposed restriction that I can't use psi amps. So I still have to deal with the alien attacks and I can't just MC them into oblivion, but I can still have psi labs so I can find my strong psi soldiers and incrementally increase their psi skill through psi lab training which will help them defend against psi attacks (unfortunately I know with the formula, psi skill isn't that helpful with attacks, but it's there).
Option 2: I saw discussions about this from 2013-2014, so I'm not sure if it's made it's way into the 1.0 version, the latest nightly, or is some kind of mod I'd have to add, but it sounded good. Alter the cost of using psi attacks so it is way higher by...
a) requiring 80 to 100% of your TUs
b) using a high percentage or 100% of your energy
c) giving stun damage so that after maybe 1 or 2 psi attacks, you're unconscious (I think 1 almost guarantees you can't exploit MC)
That would definitely tone down the power of MC for XCOM troops a TON. And it makes sense; doing these mind attacks would take a toll on the human brain/body. I'd have to do some testing and figuring out the best math (I don't quite understand the numbers on energy and stun damage), but basically you could have it so one good psi soldier could do 2 attacks every like 5 to 10 turns or something.
They only have enough TUs for one attack in a turn, then energy takes time to come back so even if they sit still it might take 2+ turns to recharge their energy and then depending on how much stun damage you apply after one or two mind attacks they are unconscious. You could have someone there to revive them right away with a medi kit, but they'd start with 0 TUs and low energy even once revived. I did some testing and it takes a lot of medi-kit to revive a person who has been fully stunned. It might take 2 turns for the "medic" (or two "medics" on 1 turn) to even revive your psi troop.
Basically the end result would be that you could use several strategically placed mind attacks during a mission and it might save a soldier or two who get stuck in a bind, but it's not going to let you MC your way to victory by taking over 10 aliens in one turn.
Even if you have an avenger with 5 psi soldiers and 5 designated medics to revive them (that leaves you a tank and 12 soldiers in the field) you might only get 10 mind attacks in a mission total. For smaller UFO crashes that's still enough to make the mission pretty easy (but at the point in the game you have an avenger, smaller UFOs should be easy anyway; they're basically just good for giving your new soldiers practice and getting some quick supplemental income) but 10 mind attacks in a base assault, battleship, terror ship or any mission with Ethereals is nothing. And that's with an avenger and several psi troops ... if you have a sky ranger and 1 or 2 psi troops, you're going to be even more limited. Again, might save a life or two or let you suicide a few aliens, but isn't winning you the day by itself.
I think I just convinced myself that option 2 would be great, but I just hope there's a relatively easy way to apply it with the current mods.