If you could be so generous so as to explain to me like I'm 5 :)
I'll mention my perspective and if you can explain why it's incorrect (if it is), I'd be very appreciative!

1. Buying back shares, I assume - has the benefit of the company (or CEO, or other head figures) retaining control over itself.
   At the end of the day, I do NOT envy the CEO who has almost no shares/say in the company and is essentially the delivery boy for the board of members (if they are many, then we're talking about a big mess). So it seems self-evident that if a company can buy back shares at a sale, it would.

2. Stocks as hedge vs inflation?
   Is it reasonable to anticipate that with inflation coming in like a high tide, that people will throw their savings in the stock market to keep it "safe"?

3. Reduced supply - higher price
   I assume here that companies buy their shares to retain control (#1). Wouldn't that mean that these stocks are then "locked up" (or at least, a lot less likely to float) and therefore, cause a rise in stock price due to lower float supply?

4. Buyback at the cost of profits/investing
   I just checked both Tesla and Microsoft, they seem to be growing in the positive in terms of profits. Unless there are trickeries that I should be aware of (can taking a lot of debt give a false impression of "profit", for example?) that hide behind the raw numbers, I don't see the issue with using excess profit for the purpose of buying back shares. If the companies were operating at a loss (or using desperately needed and lacking funds for a "side quest") I would understand this concern.

Any input appreciated! Thanks for the info