My blog has 512 posts since November of 2002. The only way using a static page generator is at all feasible to me is by not having to regenerate the site on my end.

Two reasons for this: One is that the page generation takes up to 45 seconds (with Jekyll, so punch might be faster there). The other is that if I generate locally and then want to push to github pages (having *.github.com is very fitting for a programmer's blog IMHO), every post will also create huge amounts of additional changes (I have a "recent posts" section in the sidebar) which makes for a really, really messy commit history.

So with Jekyll (based on jekyll-bootstrap), I can create a small commit for a new post and then offload page generation to github, fixing both of my issues.

As such for $other_solution to really be better than Jekyll in my use case, it must at least have that one feature that is page-generation by github pages.

Punch doesn't have it and thus, I wouldn't say that it's "better than Jekyll".