From a funk and groove-based music perspective, modes are essential to vamps and as a TBer mentioned above (apologies for not catching your handle!) are invaluable to tension and release moments due to the location of semitones, depending on what mode you're in.
E.g., Dorian has major sixth instead of minor sixth. It's a semitone away from the minor seventh in the scale. Hammer-ons or pull-offs to/from those two scale degrees are fantastic in vamps. And if you are in the third inversion with the seventh in the bass, there are even more options in the low end. James Brown's Give It Up or Turnit a-Loose is a great example (ii-V on the key of C) and of course Herbie's Chameleon (ii-V in the key of Ab), with nary a I to be seen.
In jazz and other improvised music, knowing how to support your soloist is crucial (obviously.) As @DrewD says, major with a #4 is very different from major. For me, it helps to think of the extensions. Lydian (in my translation) is M#11 instead of M#4. Yes, identical except for the octave the note is located in, but the extensions help in implying harmony above the bass notes.
Lastly, modes are invaluable in learning the fretboard. There are plenty way of learning your fretboard. For me, picking a key and going through its modes up and down the fretboard was and is crucial. And if Phil Lesh is an influence, his use of modes in improvising new basslines every night can be a great guide. Bertha is a great example. The song is in G, and the verses are in C. Not C major tho, C Lydian. Since that F# is definitely emphasized as a tension point going back to groove in G (intro, interludes between verses and choruses.)
Anyway. This message was a lot longer than intended. Hope it helps or at least adds to the conversation.