Bats with concaving will never become extinct. People want light and big edge bats and with supply of willow becoming more and more tight, the percentage of the top most grade clefts (light, clean grains, performance etc.) will become less and less.
Either people compromise - use heavier bats or accept big bats with huge edges but with flaws in the face (wider grains, some blemishes etc).
Personally, not too bothered whether the bat has concaving or not. It the balance and pick-up is good and I can time/middle the ball most times, the bat is good for me.
Except for a few most professional players don't even bother about these things.