so my above suggestion of a movement resource? I might suggest not all of them go toward teleporting around the battlefield as that would be dull.I'd love it if the mobility mechanic supported both a "teleport" type of playstyle like the 4e swordmage had, and a "mega jump" type of playstyle like a Jedi or wuxia style character.
Unfortunately the jump rules and the Jump spell in this edition aren't anywhere near good enough to support that, they doesn't scale with level, spell slot, Athletics score, or anything else other than pure Strength score. So that's not going to work.
What if there was a movement mode ability in the base class that got modified in different ways by the subclasses ? eg What if the class got a version of Cunning Action (call it something like Battlefield Mobility or something like that?) that says " You can take a bonus action to Dash, this movement does not provoke Opportunity Attacks" and then the various subclasses had things like "When you use your Battlefield Mobility, you may jump for any or all of the movement, ", "When you use your Battlefield Mobility, you blur for the duration of the movement and gain advantage on your first attack after it on your turn", "When you use your Battlefield Mobility, you teleport instead of moving normally", etc etc.
This would give them something they could use frequently but comes at an action economy cost of their BA, meaning it would contend for other uses of their BA so they have meaningful choices to make.
what were our subclass ideas again?