Well, the champions with mobility don't actually have any trade-offs for it. In fact, the super-mobile champs are often S-tier or A-tier in additional areas, especially considering the positions they're being played from. For example:
A-tier waveclear, pick potential and overall laning strength; practically the safest blind pick in mid lane and one of the very few AP champs with sustain or true damage
Strongest AP champ late game and pretty close to the same post-6. He's so powerful I feel guilty for even playing him. Clearly tied with some of the other assassins for S-tier burst
S-tier at cancer, most toxic player group in the game, always the best player on the enemy team regardless of which nexus he spawns at
I don't think I need to cover this one
A-tier waveclear, S-tier burst, S-tier split pusher among mid laners (A-tier split pusher overall) and the only champ that shows you when a target is in kill range of his all-in combo. Surprisingly, actually has the longest basic poke range of all mid laners unless you count a Varus Q (which only outreaches him by 50 units at max). Zed is also the best under-turret farmer in the game. On top of all that, he's an utterly oppressive laner who's perfectly safe to blind pick
S-tier split pusher since his update, S-tier burst, A-tier waveclear as soon as he gets

A-tier waveclear, S-tier burst, second-largest shield in the game and I think he has the largest AoE stun
This champ has literally never been out of meta or less than an A-tier jungler overall. His blatant universal superiority has been a running joke since his release
S-tier poke, totally uncontested since the Varus nerfs. A-tier sustained DPS, which is a bit surprising for a caster ADC
whenever she's even remotely playable she's totally broken. Only champ in the game that can guarantee baron/dragon secures. Best hard-engage of all Marksmen with the right support, otherwise she's slightly behind Ashe
Obviously there are more and these are just some highlights of the simplest examples. But you get the idea