I get why players want charts they can plunk onto a music stand & read. And sure, it can be educational to transcribe tunes from recordings & transpose 'em if, say, you wanna analyze a famous player's idiosyncratic riffs or perform non-standard repertoire.
Updating & maintaining a band's book of charts, however -- as I've discovered to my sorrow -- can be a pain when it requires not only transcribing/transposing but also editing & correcting, arranging/voicing, version control, distribution to new players or subs, etcetera. Chart-dependent players can easily fall into the trap of thinking that a chart is the tune -- focusing on notated pitches & durations rather than inhabiting the essence of a tune: its nuances, grooves, & saxy melismas.
As an alto saxman playing rhythm&blues tenor sax repertoire, my quick & easy way to learn new tunes is: play over recordings... memorize... improvise. Instead of tying my head into knots by interpolating named notes or keys, I simply play what I hear & riff on that.
Playing tenor range on alto is not such a big deal. I can jump an octave or find alternate fingerings when necessary. I am (notoriously) an idiot savant, so YMMV.