Jayce is not a bad champion, but he actually has several weaknesses:
A) He has not ult. This means that once he reaches level 6, there's a 95% chance that his enemy laner reached a huge power spike while he didn't.
B) He has practically no escapes. His only disengages are the gate and the hammer backslap, which may or may not work depending on how many gap closers the enemy has on him.
C) Most of the other champions with no ults (Nidalee and Elise, in particular) have Assassin as a primary or secondary role, which means that their kit is specifically weighted to overcome 1v1 situations, either through burst or out-duel potential. Jayce doesn't have this, which means his lack of ult is even more debilitating.
D) As a Fighter/Marksman, Jayce is too squishy for the Fighter aspect and doesn't scale hard enough for the Marksman aspect. He can't compete with Fighter/Assassins (who out-duel him) or Fighter/Tanks (who can contribute more to teamfights) or ordinary Marksmen (particularly the hypercarries, who are able to out-duel him extremely easily late-game).
E) He does not have significant contributions to teamfights other than a well-placed E+Q combo and a trio of W-enhanced autoattacks, given that by mid-game, it's practically suicidal to jump into a teamfight in hammer form with how squishy he is.
F) He faces an extremely disadvantageous itemisation. Rushing a Tear early means that he sinks 700 gold into something that isn't damage, mobility, sustain or resists, while his opposing laner can translate that same gold into a chain vest or [longsword/cloth/flask]+boots+pots. Essence Reaver is also horrendously designed, as it's an expensive item that works best early game (only it's too expensive, particularly if you're rushing manamune first), and by late game the passive is useless (again, particularly if you rushed manamune already). What he needs to build is all over the place: he needs standard ADC stats (AD, crit and arpen, though he can ignore aspeed thanks to his W), but he also needs mana, CDR and mana regen, and he also needs some manner of tankiness in order to not die in a stiff breeze.
G) His objective-seizing capacities are average at best. Yes, the W is great for taking down towers/dragon/baron, but that's all he has going for him, particularly since that very W means he can easily neglect attack speed items. His ability to steal dragon or baron with a well-timed E+Q combo is neat, yes, and he has reasonably adequate wave-clear, but he is a poor split-pusher given B).
H) He only has one form of hard cc (the hammer backslap) in all his 6 abilities, and it's very short duration (and short displacement).
Combine all these things together and you get a champion with no ult, who is not an Assassin, who is squishy and requires far too many stats to reach his true potential, and who has limited utility in a teamfight. He has his strengths, of course, and I've seen Jayces completely crush top lane (he does have a bit of Marksman-like scaling in that 1.0 ratio, so he can pump out a surprising amount of damage if he manages to get his full combo off on a target with no tank items), but it rarely translates into objectives or teamfights.
In short, there are other champions who do his job better. If you want a squishy top laner that deals a lot of physical damage, you have Fiora, Irelia, Pantheon, Nidalee and Jax, to name a few.
I feel I would only pick Jayce in top lane if I was facing an AP ranged caster, like Teemo, Lulu, Ryze or Lissandra. And even then, I'd rely more on my jungler ganking than my own plays. I might play him against Darius and be hyper-aggressive pre-6 and then just kite/bait him afterwards (or try to keep him constantly harassed so that he can't all-in me).
