Anything that comes in from an address I have never seen before is handled specially. But it's not hard to filter out the obvious spam. Just a handful of heuristics on the from and subject lines (e.g. if the sender's name contains common English words it's probably spam) takes care of >90% of the cold calls. The rest I just look through manually once a day or so.

I was planning to institute a system where my contact page included a special keyword to include in the subject line to get past the spam filter, but that has turned out not to be necessary so I haven't implemented that yet.

The only remaining case is things like confirmation emails for new accounts, but those just get lumped in with the other cold calls. They are super-easy to spot because I'm almost always expecting them, so they are always at the top of the list.