Mobile champions can seem to have a lack of weaknesses at times, even if they are melee. But this isn't much of a complaint as much as it is possibly a suggestion to make them much better to play against without nerfing them into the realm of oblivion.
My suggestion would be to reduce the effectiveness of tanky builds on them and then adjust their hp and resistances to give them a reasonable amount of effective health to do their job without dying. There should be specific champions that can tank and be mobile, but if all of them can, then no one is really special. Champions like Yasuo or Zed are known for being slippery, but building hp or heavy resistances only removes too many weaknesses. I believe a champion (when played perfectly) should have enough stats to do their job without dying while death should be due to either an outplay or misplay. However, extremely mobile burst/high dps champion should not be hard to kill from resistances. While to completely remove tank builds would probably be unfair to people who play those champions, this is only my opinion on how those champions should be balanced.