Sony needs people to buy it, and if the scalpers do it and resell, then Sony doesn't pay the reputational cost.

Yep. Even better, if they flood the market with additional units and sell them at the same price, it's the resellers (scalpers) take the hit, and not them. Sony is probably selling them at a loss and intending to make it up on the software (game) sales. This means doing anything to decrease the demand, even a little, reduces their ability to make money on the part of the business that is intended to make the money.

Sony is losing a lot - their customers are paying a huge "tax" on top of their product price and Sony gets nothing of that.

the idea is that they won't stop buying it. If they would, then the price from the bots would be lower.

As someone above pointed out, Sony is concerned about the entire 5 year cycle of the PS5, not just the current quarter or even first 18 months. There is also the need to maintain customer goodwill for the future PS6. There is already a fair degree of substituteability between a PS5 and Xbox. By the time the PS6 is out there will probably be a Steam Deck 2.0 and maybe something new with Nintendo.

It's far better to let the scalpers take the reputational hit.