Yeah. The symmetry can help a designer notice a possibility that wasnt considered earlier. But it gets in the way when becoming forced.
Also, the symmetry depends on how useful the components of it are in the first place.
For example, D&D and many derivatives of D&D, completely rely on the six abilities. But these six merit critique, in the first place.
For example, Wisdom began as a narrative concept, "being wise", but in practice, this concept has poor mechanical application. Where use is meaning, Wisdom now means exactly, the five senses in a way that animals tend to be good at, or else willpower to resist mental attacks. Defacto, this ability is incoherent at best. Personally, I would just give Perception to Intelligence, and give willpower to Charisma. And be done. There is no reason for "wisdom" to exist as an ability. The Cleric is a spiritual leader and inspires and is inspired by other persons, thus is Charisma. The Druid understands nature, thus is Intelligence. We only need two mental scores, and there is no loss of information. Likewise, the three physical abilities lack an ability that simply does athletic stunts. It gets disruptively and implausibly dislocated, as if people who know how to jump are unable to tumble, and people who know how to climb are unable to know how to catch oneself from a fall. The current six abilities, both the three mental and the three physical, feel off. Like a rickety car engine that is making worrying noises.
