How would Jhin support work?

Bad. That's how.

You could try it but it wouldnt be very effective. Because you wont be getting much gold which means you wont get that many items, plus you gotta buy a sightstone. So, (other than the first 5 minutes) you would do virtually no damage.

Just go AP Jhin lol At least he still deals alot of damage with his traps if they are close together.

You would have a decent lane I imagine, but you would scale horribly into late game with your only usefulness being the slow on your traps and ult.

If you want strong poke and free wards as support go with Zyra imo.

too much mana cost

He would be bad late game as he'd be an immobile squishy with no damage and relies on the team to hit stuff in order to stun, and his ult is execute damage. Definitely not the worst champion to support and it's not like you couldn't, it just wouldn't be good.