The mechanism is mentioned by another, but the idea is that higher interest rates reduce the present value of future cash flows, resulting in lower asset prices

The mechanism is mentioned by another, but the idea is that higher interest rates reduce the present value of future cash flows, resulting in lower asset prices. However, this analysis is holding everything equal, which is not true in real life. For instance, if higher interest rates are due to higher inflation expectations reflecting stronger nominal growth, then some assets might do better in such an environment. Your second argument is that it would be trivial to stop and reverse inflation if it were true, but even if it were true it would not be so easy. The way we measure inflation is based on the prices paid for goods and services of consumer goods. If the only change from an interest rate hike were on asset prices, then this doesn't directly impact prices of consumer goods.