Part of my argument is that there are TONS of great jazz tunes from every era - even now, we are NOT hurting for music to play - we can even (obviously) improvise freely. The great compositions now are not written by Nirvana and Radiohead but by David Holland, Anthony Braxton, Kenny Wheeler, etc., etc.
I think that's a very narrow point of view. I'd say both jazz musicians and pop/rock musicians are writing great compositions. It doesn't need to be either or.
What is inarguable is that pop/rock musicians are writing music that is much more culturally relevant. This will lead to jazz musicians covering these tunes for a couple reasons. One, and most obvious, is that a cover of a popular song (or a song by a popular artist) draws in listeners you may not get otherwise. Two, and more often overlooked, is that jazz musicians don't exist in a vacuum. If an artist is popular or a song is culturally relevant then it is going to influence artists from other genres. This can lead to some inspired music.
Finally, I look at a lot of the cross-genre covers that jazz musicians have been doing as a great way to hook non-jazz listeners on jazz music. Someone might buy a The Bad Plus record for a cover song they like, and if they like the record they'll dig deeper and be exposed to Bill McHenry, Tootie Heath, etc. A Radiohead fan who bought Christian Scott's last record because there was a Thom Yorke cover on it could very quickly find themselves digging through Donald Harrison's catalog.