Say you fire half the managers. Let's say you live in a fantasy world where you can accurately measure who is the bottom half vs. the top half by whatever metric matters to you. So you fire the worst half. You've just done a couple things:
1. Probably triggered some sort of "layoff" legislation/notice/severance/whatever and sent a ton of people looking for work before the next round, whether you expect there to be a next round or not (but you've already said there would be).
2. The good managers, who could probably walk into another management role without much trouble, do so. Why risk being in the second round?
3. You're left with something approaching the middle quartile, but now they're doing more than 2x the work after the top 5-10% of your management leaves after your purge. How many people do you know suddenly get better at their job after you double their workload?
4. I don't know how true it is but there is an old saying "people don't leave jobs they leave managers," and so now for half the company you've fired their manager and given them someone very overworked. For some non-trivial percentage of the company their new manager is worse than their old manager.
5. Due to #1 and #4, your best ICs start to leave, so engineering and product quality (and velocity) drop precipitously.
6. You've lost your best managers, who would fight to keep the hiring bar high, so the weak ones compromise on shaky candidates. Engineering and product quality drop even more, and morale tanks.
Congratulations, you've just filed for bankruptcy with extra steps.
1. Fire 50% of managers. 2. Use the salary money saved to hire people doing the actual work. 3. Wait for a while to see how much things have improved. Repeat if overall performance has improved (it almost always has).