Let's Look at HEALTHY Mobility
Everyone complains about the Lees, the Zeds, the Jarvans, and all the other champions that have mobility that don't pay enough for it. Yes they are a problem. However, there are quite a few champions that do pay for their mobility in ways that give them meaningful weaknesses. Let's look at them and see what we can learn.
This guy has a dash on a moderate cooldown. However, he is melee and his only skillshot is both slow moving and short range. He has sustain and a great passive yes, but he is very vulnerable to skillshots and kiting when his dash is on cooldown.
This sad guy has huge mana problems in the jungle, or so I hear (haven't played him myself). His biggest asset (ultimate) is on a long cooldown and he doesn't deal insane damage.
his q makes him fairly mobile, and he brings quite a bit of crowd control to the table, with his passive, his Riptide and his Depth Charge. However, like Amumu he has mana problems and doesn't deal tons of damage.
This guy doesn't have a dash, but his w can give him almost 600 movement speed with boots. He is very strong with his stun passive and ultimate, but he can be kited and is very vulnerable to slows. Just stay away from him!
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These guys both pay huge resources for their mobility, and those abilities are on a lengthy cooldown. Kennen is very strong yes, but he has definite counterplay, being low range.
This champion is extremely strong at the moment, but her kit is well designed and she has easy potential to be balanced. Her mobility is telegraphed and predictable and can be interrupted. I think she could be brought back in line with a more meaningful cooldown on her insane ultimate.
Obviously these guys are not all of the mobile yet balanced champions out there. I just wanted to list a few different playstyles that incorporate mobility while retaining meaningful weaknesses and are not overbearing. These types of kits are great examples and should be looked at for the purposes of balancing the hypermobile offenders.
TL;DR: Many mobile champions have great kits with meaningful weaknesses, and the mobile champions that lack weaknesses should look toward these for their counterplay and balance.

