The more the leathers lift from the reeds, the less responsive the box becomes. Notes will start more sluggishly.
If you are not a fast player, it may not bother you at all.
But the leathers are also there to protect the reeds from air passing through them "backwards". Too much air going the wrong way can put your reeds out of alignment so they do not respond well, and also reduce the useful life of the reeds.
If the leathers are too high you get a little floping sound when you play that reed because of the delay on closing. However those leathers don't seem to need changing just resetting which after being done may require some retuning. Pretty minor but may cost a few bucks.
Is there an easy way to straighten the leather back out flat? Any one have a secret technique other than replacing the leathers? I have also found that a gapped leather can also cause the adjacent reed to buzz before seating.
seems like you could heat one side or the other
but i wouldn;t know which side to heat
you could experiment with some non-accordion leather
if you needed to heat the back side, that
would be harder
but not impossible
or just remove it, fix it somehow, with heat or
manipulation, and reglue it
Here's a traditional fix...spine the leathers. You can do this by slipping a reed lifter or other thin metal strip under the leather, and using a pointed but not sharp awl to scribe a line down the middle of the leather. This gives it some structure and helps keep it flat. The leathers on the Martin don't look bad to me, though.