It's a complicated relationship, but yes stocks generally perform well in inflationary environments, certainly better than bonds which unequivocally get crushed. However, often what happens along with rate increases is tighter lending standards, increased borrowing costs, less ability to refinance at attractive rates, etc. It's also more difficult to raise equity when investors have reasonable alternatives in other asset classes. Suddenly investors start caring about tired and old things like "valuation" again, and "price to eyeballs" or "tweets per minute" matter less.

For companies that have been riding the wave of free money in perpetuity, that's a bitter pill to swallow - when it's time to refinance they aren't prepared to pay the new bill. More dangerously, they simply may not be able to refinance at all if credit markets dry up (2008), and that is when it gets really ugly.

Stock prices are as high as they are right now because there are no reasonable alternatives. It's the "least bad" option.