That's the number one reason I would like to run my own server. (And, no, the Gmail trick of adding "+foo" to the username doesn't satisfy me because spammers know this trick and can strip it.)
Quickly add a new forwarder and feed the service that email address instead of my normal address. When they turn out to be spammy, the forwarder gets removed.
What ESP do you recommend for unlimited (or large numbers of) aliases indistinguishable from individual email addresses (such as ycombinator4853@foo.com facebook843983@foo.com but not john+ycombinator@gmail.com john+facebook@gmail.com)?
Edit: fastmail's standard $50/yr plan offers 600 aliases. This might be good enough. I've created online accounts at 371 different services over the last 20 years.