What is the best way to deal with cranks?

Ignore the crank.

Unless you are in some location where you are required by law to respond to communications (I remember reading here about one country where it was indeed the case that it was required to answer emails as part of "open records" laws), you are under no obligation to waste your time on a crank's musings.

If it amuses you to respond, feel free to do so, but you waste your time at your own peril!

Follow the peer-review model with some tweaks:

If the work is clearly flawed and so off the mark that nothing can come out of it, ignore. [Desk reject]

If the work may have some iota of sense, but it isn't worth your time to get into it, write back suggesting a different forum, like a blog post. [Reject and suggest transfer]

If you are marginally interested, but not sure whether it's worth it, ask them to try presenting it better/differently with more proof. [Reject and resubmit]

If you think it deserves a chance, but can't get into it yourself, lightly share with your colleagues/students over the coffee table and if anyone seems interested, let them take it up. Alternatively, as suggested by @jpmc26, you could ask them directly if they would be interested to detect preliminary errors that could be pointed out. Purely voluntary, of course.[Assign reviewers]

This happens far less frequently than inappropriate requests for postdocs that have absolutely nothing to do with your area, invitations to participate in conferences that have nothing to do with you, invitations to serve as section editor on predatory journals, .....

Handle them all the same. Use your delete button.

A call or visit is harder to deal with. A polite "... very interesting, but I don't have the time to follow up on this" might get you off the hook. If the person shows up at your door more than once, I recommend calling security.