I can't think of anything else than some arcade games requiring the lowest possible latency. People are okay with 50 ping games so 2 ms really doesn't matter to most players.
50ms network latency is not the same thing as 50ms controller to display latency.
If your network latency is 50ms, you still have extremely low, almost zero latency for most operations like using the mouse to change the look direction.
50ms display latency would make a modern FPS utterly unplayable.
It's not just SSB. There are entire classes of games that aren't playable even at novice levels on modern LEDs like Guitar Hero style rhythm games.
LEDs often have much higher latency than necessary. Many have ALLM modes which disable certain features to decrease latency. We already have changed LED technology for this reason -- higher end computer monitors specifically focus on latency now. It's a really big deal.
LCDs may refresh pixels at a rate of 1ms, that does not mean the pixel displayed is only 1ms away from the input. You can get maybe 10ms of input lag with the very best setups. Modern TVs easily have 100ms of lag out of the box due to processing which you may or may not be able to bypass.
The traditional way to play melee is local multiplayer only, so players most players are used to the incredibly fast response of a CRT. This and the muscle memory required to play at a high level makes LCD monitors (and especially TV's) noticeable.
If your network latency is 50ms, you still have extremely low, almost zero latency for most operations like using the mouse to change the look direction.
50ms display latency would make a modern FPS utterly unplayable.
Games like SSB are extremely latency dependent.