Champions with no haste, no mobility spell or effect, and low base movement speeds are pretty rare.
The only champions with 325 base MS and no mobility are Ashe and Anivia. Every other champion in her movement speed bracket has a haste, dash, blink, or at least a conditional haste. The only such champions with 330 base MS are Lux, Syndra, and Varus. 335: Annie, Malzahar, Morgana.
Every one of these champions is a very safe laner, a lane bully, or both, and has lots of reliable crowd control and a good late game. Only Lux and Syndra ever really fall out of the meta, too, leaving the other eight champions reliable in any season. I think they’re pretty strong.
The ‘mobility creep’ meme is just that. All melee champions have gap closing mobility or long engage range, and they’re half the roster. Many ranged champions are at least semi-mobile, like Taliyah, or conditionally mobile, like Jinx. Pretty much all champions have some way of moving faster than a walk, and Riot has been designing them to have one from the beginning.
Edited to Reflect Comments!