Comic book Batman also knows that killing the Joker isn’t going to stop him for much longer than locking him up.
More seriously, as someone noted up thread, while the Joker may have escaped from Arkham dozens of times since 1940, in any given contemporary comic, the Joker has only been around for maybe ten years, tops. So not all of those escapes can be in-cannon at the same time. My head cannon for Batman books is that in any given appearance by the Joker, he’s only escaped from Arkham twice, maybe three times, and that that constitutes a record for inmates there.
The reason the Batman doesn’t kill the Joker is because he knows that if he started killing off his special guest villains, the A-list stars would stop accepting invitations to appear on the show (taking Batman too seriously can cause you to WAAAAAY overthink these things).
BUT, if you simply must insist on looking at Batman as other than the beloved character portrayed by Adam West, sure, I can play along for a bit.
Okay, let’s say that Arkham can’t hold the Joker. And Batman can’t bring himself to kill the Joker. Why can’t Batman hold the Joker? Surely, he can build an escape-proof cage in the Batcave and keep him there.
If Batman is worried that the Joker will figure out where he is, he can always put the Joker’s eyes out.