You really just don't get how the Renekton VS Jayce matchup plays out.
Jayce sits in ranged form, pushing in the wave and denying ranged creeps with autos + ranged W. Renekton tries to sustain it with Q spam.
Jayce never needs to use abilities unless Renekton goes for a fight.
In order to go for a fight, since Jayce is ranged, Renekton has to utilize his E reset. What Jayce has to do to counter this is switch out of cannon into hammer and E renekton all before Renekton can finish the dash and get into his W animation.
The mistake a renekton player can make here is giving Jayce extra time to react by trying to auto + W in the combo.
Back to the trade: Since Renekton's hitbox doesn't move forward until the dash is entirely completed, a well timed Jayce E will knock him back from the ORIGIN point of the dash and then the full distance of the knockback.
The way to outplay this as renekton is to wait to dash until you know jayce is locking himself into an attack animation on either you or a minion. that split second of extra time you get is usually enough to get a W off and then dash behind him before he can E you.
The agency to win the trade lies ENTIRELY on Jayce to predict when Renekton will jump in and attempt to knock him back.
Dashing in as Renekton is not the mistake since it is your ONLY way to equalize lane presence, and Jayce will NEVER have his E on CD when you have dash (at least at / after level 3).
Is the Jayce lane unwinnable? No.
Does Jayce have an advantage in the lane based on kit interactions? yes.
On the note of not knowing how to manage / keep track of cooldowns, I will reiterate that the cooldown between Renekton and Jayce E is that they counter eachother and get used at the same time every time in an even skill lane. As such, there is no abuse window between the two untill level 10+ when Renekton really starts sinking points into his E.
Yes this matchup is decided by mistakes, but they are mainly mistakes that are up to Jayce to make. If he doesn't knock me away when I dash on him, that is HIS mistake. Me dashing on jayce when he has E up is NOT a mistake because of the cooldown interaction between my dash and his E.
Yes, league as a whole is decided by mistakes, but some matchups leave all the agency on ONE champion, and almost none on the other.