Jazz tunes ending on weird chords?

What he said. Lots of tunes that aren't bebop end on jarring chords too, presumably because the composer wanted a jarring ending rather than a comfortable, expected one. I don't think there's much more of an answer to the "why" of it.

There are lots of things that are "incongruous" in a traditional sense about bebop, though. There's a nice rundown http://en.wikipedia.org/wiki/Bebop#Specific_harmonic_vocabulary.

there's nothing more traditional and recognizable than a V-I or IV-I cadence. One of the things Jazz is known for is resolution and cadences with extensions or deceptive cadences. Extensions are non-chord tones that stack within or on top of a chord to add color. Deceptive cadences are just that--they go in a direction not expected by the ear. Aside from what's mentioned above, this may be another possibility.

So everyone knows, it's the end, for real. With lots of jazz, you're flying fast. The end doesn't fit because you smacked into the wall of the end of the song. It helps pull you out of the grove you've been in, too. Maybe modulating towards the next tune in a set?

Yep, "traditional cadences are for squares" - not just in the sense that they can be boring, but they're so expected that they almost sound wrong sometimes. Random chords - that's fun, so even though the harmony may sound incongruous in the theoretical sense, the wackiness is just part of the good times.

What's funny is that there "incongruous" bebop endings are completely standard. Go to any jazz jam and, if you're a bass player, put a big fat IV on the bottom of the last chord. People will smile at your cleverness every time. Make it V or VII and they'll think you made a mistake.

Because it's fun and unexpected, as others have said. However, consider that ending on the tritone of the tonic in the bass happens frequently, which combined with some normal extensions, can sound pretty weird. Mike Stern's "Like Someone In Love" on "Standards" ends with an E in the bass and some lydianish stuff (9,#11, 13) for the tonic of Bb, so you've got a D triad on an E, unless my earmemory is mistaken. But it's also true that some jazz songs I've played and composed just demand something unexpected at the end. And in my experience it's been to wake up the audience at the end of the tune. YMMV.