But you said, that's not how it works --> that would be in a way to emphasize the bad side of it, which is high hash rate means more machines and more energy, and more expenses. If it exceeds the profits then obviously the business will go bankrupt.
The result of halving is reduced hashrate not a higher one.
The price of Bitcoin does not instantaneously rise after the halving is done, but the new coins awarded to miners is halved immediately, causing miners with a business to run to encounter difficulties finding their mining gear and electricity.
By history, many miners lose interest in mining immediately following the halving and close down their rig. This results in a lower hashratr and some period of difficulty adjustment to make it more accessible.