Neither has locking them up

You need to read it in the context of the other strips. Normally, someone in the first panel defies Everett’s sense of decorum and general decent behavior (e.g. describing a way they took advantage of another person, or being unecessarily), and in the second panel Everett cartoonishly attacks them in a fit of righteous rage. It’s all meant to be a wish fulfillment for someone struggling with the stresses of “modern” urban living. I feel like Larry David would probably have been a fan if he were around during its run, if that helps; just imagine the Seinfeld gang if they looked and acted like Kingpin from the Marvel stuff. I think the audience is invited to sympathize with Everett’s sensibilities and to laugh at the catharsis of someone actually indulging their rage.

This one subverts the trope. It invites the audience to suppose the beggar will be destroyed, especially with the foreshadowing. However, simply existing and hoping for a little generosity does not violate Everett’s personal code, so going against the perceived rational choice, he listens to his better angels, leaves a coin, and moves on. I can almost imagine the cartoonist starting to become a little troubled at how sincerely people, possibly total assholes, professed to admire Everett and so wanted to turn things around a bit.

He tried his best to ignore the beggar but couldn’t because he has a heart of gold. It’s more wholesome than funny this time.

I guess the humor is also that he’s frequently violent in all of the other comics but can’t help that he’s actually a big softie.