Kha, Rengar, Diana, Kat, Qiyana, and Sylas not assassins now? They don't really have escapes.
Kha can run out under invisibility. Qiyana can run out under invisibility and I think her dashes are low enough cooldown to get out. Kat's dashes are on a more than low enough cooldown and she can dash to allies.
Diana and Sylas were designed as bruisers and are literally not assassins. Diana is no more an assassin than J4 is.
Ahri ISN'T that mobile though. She doesn't have free mobility on any of her abilities. She has to use her ult for any form of mobility, unlike every other assassin in the game besides Eve or, situationally, rengar.
Are we back to using "free" as a buzzword again?
Warwick, Shyvana, Sett, Zoe, Malphite,
All of these have only one dash. Sett's moves forward at only about his fucking walking speed. Zoe's is only a temporary displacement. Shyvana's is short range. Malphite is otherwise very slow. Warwick's the only one you could consider mobile out of that bunch, and that's because he's just fast as fuck.
Ahri has a significant speedup on her passive and an ult that goes significantly farther than any of theirs (except Warwick in some situations). Sure, she's not hypermobile, but it's still more than what could have someone actually considered a mage.