Not mentioning it while talking about acrobatics doesn't mean that I don't think that athletics should also be split more like it once was. Those two skills are not alone in their need to be redivided. Once the over consolidated skills are split and mechanics are built around the existence of that split it allows quite a few classes to invest in areas they would not normally under the current pick any* 4 skill systemWhen we are talking about the Strength Ability, the only classes that benefit are Fighter and its historically related classes Paladin, Ranger, and Barbarian.
It can be Paladin emphasizes spellcasting Charisma, Ranger goes ranged Dexterity with finesse or Wisdom spellcasting, and Barbarian doubles down on Constitution toughness or Charisma primal magic.
Thematically, the Fighter class is the most likely class to invest in Strength and its Athletics concept. It is mainly this class that benefits from the agile mobility concept, because it already has the Strength investment. This is already at the opportunity cost of losing out on the strictly more optimal Dexterity Ability with its ranged, high AC, and finesse two weapon Fighter, or also losing out on especially tough Constitution or perceptive Wisdom.
There is no optimization gain by consolidating agile mobility. It is a correction of a self-harming D&D design that kills the swashbuckling concept before it is even born.
*The bar to picking beyond the explicitly allowed options and any skill is so low that players sometimes need to work at being limited to skills they don't want on their pc