Bold of you to say that Jazz is 'pretty repetitive.' Basic standards that everyone knows which aren't complex.... sure... no need or excuse to have a chart. BUT -'standards' - while originating from set forms generally derived from the venerable ii-V7-I progression and permutations of it - are not always what they seem, especially if the pianist or guitarist is throwing in substitutions which aren't easy to ear out perfectly. Also, there's plenty of 'Real Book' material that's trickier than one might think, especially if it's a singer doing a tune in a new key, different reharmonizations beyond the 'stock' progressions, and any songs that are not 'typical' progressions (like a lot of more modern jazz that's now part of the canon). If you're doing original jazz, and you're the composer, then asking someone who hasn't done your music before to do it without a chart on the fly is not cool.
I guess Jazz 'seems repetitive' if you're not hitting every change, or are winging your way through it with just roots.... or chromatic wandering to get through fuzzy parts. I'd rather have a chart on hand JUST IN CASE, to make sure the music doesn't sound amateur, versus not having one just because of an egotistical need to not be seen with a chart somewhere.