Is medic a less popular class in competitive TF2?
Perhaps yes, it's not a class for the standard fps frag focused player, but some like to be counted on and as such medic can be popular. It's like in all the MMOs or mobas where supports are needed : feeling valuable when you play the role is rewarding in itself.
Are valve attempting to encourage people to play medic by making it more powerful? Is it working?
All I can say is that i don't see more pubbers play medic than before the update. But in matchmaking everyone seems to recognise the need for medics, so at least this part is working.
As for medic becoming more powerful, i don't think it is needed.
Would it not be better to re-work the medic to make the mechanics more fun (such as the crossbow?
Is there even a problem here, or is this all just my gripes as a medic-main?
There is no problem. A lot of fun mechanics are already there : crossbow as you said, quick fix and vaccinator are all fun and rewarding to use properly.