I disagree sightly. Producers I've worked for on rock/blues sessions have said that many session players haver a problem with playing other genres. I've known so many jazz players who think dismiss blues as easy, and yet without being able to play blues convincingly. They get the harmony yet somehow miss out on the feel and intonation. Somehow unable to leave the jazz licks and patterns at home.
There IS always THAT. You mentioned here once that Joe Jackson chose you for Jumpin' JIve because you weren't deep-diving into 'serious' jazz licks and such, but rather staying more with the Jive genre, feel. (I paraphrase here, but I think that was your gist).
So, yeah, there is that danger. Jazzers can tend to do that. I once shared what a sax player I used to play with in San Fran told me, when he played blues and rock shows - "sometimes those bands tell me "hey, knock it off with the Coltrane sh#t".
I was speaking to it more from this perspective, however:
Jazz requires a player to be pretty honed in on a lotta stuff...ear training, theory, phrasing...a few examples.
So when they (we) have to decipher a tune for an upcoming performance, say given only a playlist and maybe a chord chart or even chord tabs....we can do a better job at hearing what's going on and getting the gist of a tune than musicians who are not half-decent jazz players.
Quick proof of this....the PLETHORA of chord tab sites and sources across the 'net where people have (ostensibly) decoded the chord changes from songs to which there are no (easily) available charts or publications.....
I hope nobody here has had to spend a whole lotta time using those chord tab sites as a resource (I have, yipes)...because really....90% of the efforts that get posted and (ostensibly) circulated...are so BAD, so incomplete...that besides maybe being useful for providing the ROOTS of each chord...they have little value at all.
So in this instance, a jazz guit or pianist, say, can do a transcription which is WAY more accurate than what a garage band guitarist (even a gigging one) came up with.
Example 2 - when I was in a funky rock band, again we had to source our music from original recordings or covers, mostly did it thru YT. A lot of times the material we chose, while GOOD songs, to me were only, say, 3/4-baked. They were catchy, people recognized them....but we wanted to do more than just a copy of the original....a lot of them had more potential to become (for fear of sounding hoity-toidy) better or more interesting than the original.
Yet when I would look up covers of such tunes on YT, I would say...70% of the covers I came across, basically displayed the band (at best) performing the song true or near-true to the original...or...doing a really rudimentary interpretation and being perfectly ok with that. Yet pop songs can be mined for more than that, IMHO. And players with some jazz sensibilities seem to be able to do that...again, apologies for my bluntness...'better'.
So I meant it more in that sense. I do agree, sometimes jazzers do try to shoehorn their style into a genre which isn't calling for it, and sometimes they ignore other aspects such as rhythm or general feel.