Experience is more relevant to whether the mechanics are working, because working is a matter of satisfaction, which is inherently experiential.
That's fine! Nobody can say that someone's experience isn't their experience, and clearly there are people who have an enjoyable experience playing monks! Saying that they are low power doesn't undermine that. But we ought to be able to have both! If it is true that monks are underpowered, then it naturally follows that they could use some buffs. The
nature of those buffs definitely needs to take the subjective play experience into account.
We may not want to buff monks by just giving them flat damage boosts, and we may not want to buff monks by making all their abilities at-will, etc., or buff their survivability by giving them armor proficiency, or making them viable only if they use weapons, etc., even if we worked out ways to do these things that put them on par with other classes, because clearly people who play monks want the 'equipmentless' playstyle that forces tactical tradeoffs. But buffing them in a way that makes their action economy less clunky, or makes certain abilities have different opportunity costs besides ki expenditure, or sets them up to still be reasonably effective at offense when they prioritize defense or control, and vice-versa, would help, and I don't think it would undermine the experiential aspects that draw people to monks.
But even beyond that, many of the things that are harder to quantify are mechanics. Moving 20ft further per move action at no cost is a mechanic, it impacts fights and exploration challenges, and it’s hard to quantify in a white room because it is very hard to plug into an equation without running a thousand simulated scenarios first. But, when most people who play monks say that they often end up the star of a scene because of their speed, it’s hard to take seriously an analysis with a strongly held conclusion that doesn’t take that into account.
It's absolutely a mechanic! And it should absolutely be factored in! But mobility is only useful in tandem with other strengths. That a character is able to move really fast doesn't do anybody any good
in itself, but it might if as a result of their mobility, that character is able to affect enemies, or prevent them from affecting the party, etc. But that's something we can take into account, and
quantify, in an analysis. The analysis won't perfectly reflect the in-game reality, but it's important to attempt it and refine it if we want to know whether buffs are called for or would create problems.