Maybe a lot of these international brands exiting is more useful than some of the other sanctions. It hits the more wealthy, who lose a sense of status and feel left out of the world. That can't be good for Putin who is seeking glory.
I'm sure the PR hit they'd take from continuing to do business is a factor, but I don't think this many large int'l companies would have reacted this quickly to just PR hits.
All international companies really, really, really, really like to get paid for the goods and services they provide. After sanctions that becomes difficult to impossible to do in Russia.
I think their thought process is:
Best case scenario they get paid in rubles which have gone down in value and are likely to go down further or at the very least be very volatile.
Worst case scenario they get $0 USD for their goods and services as they can't get the money out... and they are slapped with further sanctions.