Algorithmic password generation from a single master password works fine up to the point where it doesn’t. What happens when you run into a site that won’t acc

Algorithmic password generation from a single master password works fine up to the point where it doesn’t. What happens when you run into a site that won’t accept your algorithmic generated passwords? Do you fall back to a traditional password manager? If so, then you’ve just increased your attack surface area by an order of magnitude. What happens when you need to change your master password because of a compromise, and now all of your passwords have to change at the same time?