(The good news is that it's not really expensive to pay someone to do if you don't really need the services of a full-blown editor who is advising on structure, flow, etc.)

Agreed, but it's easy to hire a freelance copy editor. In fact, that's often what traditional publishers do too.

IMO, it's not something you can rely on software for although software catches a lot of course. The one time I didn't do it worked out OK. But I had a co-author and we had sufficiently reworked the (somewhat shorter) book enough times over a fairly long period that I decided it had had enough fresh eyes on it to stand on its own.

And of course publishers aren't perfect either. I've found a few typos in my last book which did go through a traditional publisher even though I also proofread it pretty carefully. (One mistake was in front matter which I added fairly late on which makes me suspect there would have been a lot more errors in the book if I didn't check it carefully myself.)