Daredevil is a vigilante, what do you expect him to do? Dude had already committed a violent, public-endangering crime, so why let him go so he can do it again?
I dunno, track him back to his boss or lair or wherever he's going? Attack him when he can do so without maiming him so brutally and psychotically? He had all the options in the world at that point. The guy was not an immediate threat to anyone and didn't even have any stolen goods.
Also, this needs to be read in a both Watsonian and Doylist way, and it's just shenaningans to stick solely to the Watsonian angle as you're doing. The writer/showrunner of this episode (almost certainly NOT the current showrunner) decided that insane hyperviolence against a man who was considerably less bad (as far as DD knows, anyway, including what he overhead) than many people DD faces off against was the correct for this story to go. That's a bizarre decision, and at-odds with the general tone of both that episode (which was fairly whimsical) and the entire Daredevil TV canon, where DD is
not a psychopath, and doesn't do that kind of thing without an extremely good reason and when he does, it costs him personally/emotionally unless its life-and-death (and sometimes even then). Also, it blurs the line between him and the Punisher in a way that's not clever or cool, and that I'm sure wasn't intentional (again, given the tone of the rest of the episode). DD doesn't generally "punish" people for distant sins, he takes down people who are immediate threats or who are really serious ongoing threats (which one fleeing bank robber certainly doesn't qualify as). Absolutely brutalizing the hell out of a guy who hadn't actually done anything horrific and was fleeing should be significant for DD, especially when it's clearly not some particularly life-or-death fight for him.
They could easily have worked it in as him losing control, or him sliding towards being a Punisher-type and having to atone for that, but the episode totally did not do that, instead forgetting that brutality and immediately engaging in as I said, almost 1960s Batman levels of silly business (which is pretty off for Daredevil, sorry, but it is).
Further, there's a pretty clear plothole (unless it's acknowledged or followed up later, I haven't seen the newest episode yet) in that at least one of those bank robbers 100% knows he got beat up by that blind lawyer guy (unless he's suffering from head injury amnesia or something), and I'm sorry, this isn't grade school, he's not going to keep that to himself out of embarrassment or something. Especially as evidently someone did it, and there are no other suspects. So given that and the wild and clumsy tonal fluctuations, I think this is a pretty clear example of the dreaded "bad writing" (but again, not by the current team working on DD, by the old, fired one).
