AP assassins exchange safety and range for that mobility.
Le Blanc may be able to access her damage easier and more often than Lux, but she cant safely harass nor pick off targets from 2000 range.
Fizz, Nocturne, and Diana's damage is heavily gated and they're all melees.
Ahri is more of a mage than an assassin, but the lack of reliability in her damage (Charm only hits 1 target, W and R target themselves, Q is easier to dodge than it is to hit and the damage is backloaded) enables her to have some AoE, and her mobility is gated behind her Ult. In return, if she has her R up she has all of the qualities of typical assassins, amped up beyond what would otherwise be appropriate for her kit.
Ekko is strongest if he can land his skill shot, but he's also crippled by snares and his damage isn't quite as high as other assassins until he gets massively snowballed. in addition he IS melee, but his E and Q helps him against ranged champions.
AP Rengar is actually less bursty than AD but has different advantages.
[{quoted}](name=Metal Janna,realm=NA,application-id=3ErqAdtq,discussion-id=xzs1L8Ek,comment-id=0000,timestamp=2019-08-22T21:07:18.309+0000)
AD assassins have busted mobility too.
Mobility creep is real, but so are damage creep and healing creep. Riot only knows how to deal with things being OP by buffing their counters.
... Riot does anything BUT buff the counters to things. Ever heard of Sejuani? Olaf? Aatrox?