Exchanges already have whitelists

I don't think covenants make them worse

The recipient creates the covenant, not the sender, so just don't create a covenant that restricts how you can spend your money

If your concern is that exchanges might require you to create a covenant address that matches their template, otherwise they won't let you withdraw, they can already do this thing that seems equivalent:

Exchanges can -- right now -- only let you withdraw to a 2 of 2 where they control one key

Then they'd get to veto any future expenditure you try to make

Are covenants worse than that?

Even if they are, just fall back on this: don't make a covenant encumbered address and exchanges can't harm you (except by refusing to send money to you, which they can also already do)