I think we'd all rather "sift through a little spam than lose something I wanted" but my guess is that you've never run an email server. "a little spam" is not what you will get - it will be orders of magnitude more spam than legit emails. This is hard stuff - Gmail, supposedly one of the best, catches between 2 and 10 emails a day in my "Spam" folder that aren't actually spam. If I were to turn off the spam filter (if you could) in Gmail, I'd get 2,000 emails a day - of which 50 would be legit.

I actually have run a mail server before, and now I gladly pay someone else to do it for me :)

Point taken, but I've been on the receiving end of what I would consider false-positive blocks by Spamhaus & co. They sometimes have policies about what's considered spam that I don't think all their end users would agree with. I've been blocked for having an IP address on the same provider as someone else who allegedly advertised their website via spam. If you're running a mailing list, dealing with the anti-spam stuff is at least as big a problem as the spam it was supposed to solve.

Then use greylisting only.

I've never had a case of a false positive complain but yes, they can happen and I don't terribly mind because that means the sender's mail server is blacklisted and they should know.

Also in any case my recommendation is to use a 3rd party mail service, for deliverability reasons mostly.

Currently, I get a couple thousand spam messages a day, maybe 5 of wihch make it to my inbox. I haven't had a false positive in years. But if I did, I would be ok with not having to manually evaluate 50 pieces of junk for every real message I receive.