Stats with proc rates like Crit and DH create variance which has some impact but how much of it you feel varies a lot by situation. On a boss with a lot of HP they don't change the feeling of gameplay at all because everything averages out. In a short DPS phase (adds, boss charging up a mechanic) a lucky string of crits can noticeably speed things up and can change the feel or combat, though I prefer when player agency is responsible for significant changes rather than rolling dice. If raising Crit/DH rates was only a potential burst gain and not an average damage gain they could have offered a way to tailor a character to certain situations but as it stats Crit and DH have no downsides so there are no choices to be made.

Piety gives the player a dial to turn to tweak performance (DPS) vs risk (running out of MP due to unexpected healing) so there is a choice to be made here. Again I don't think it's very meaningful though. All it does is raise your parse number which doesn't make gameplay feel better in my opinion. I also think that healing when things go wrong is the more fun part of healing so optimization in this case would make things more boring.

Tenacity giving a slight damage reduction can make a difference though it's the healer that will feel it more than the tank. I think tenacity would be more interesting on non tank classes, but at the same time, with the way damage works in this game it would be really hard to justify using. It's already hard to justify on tanks.

The speed stats are by far the best ones because they change how classes feel. From a gameplay perspective these are the only stats I care about. They also come with tradeoffs. Faster casting means more MP use and potentially less raw damage. Dealing with tradeoffs like this is one of the hallmarks of good stat design.

Overall I don't think the stats in FF14 matter very much. Speed stats are good. Piety and Tenacity are kind of OK but not valuable. Crit/DH/Det are the most important stats but very dull. If stats were changed to allow players to change the feel of classes I think it would be a better system. That stats would need more tradeoffs. Fight design shifting to something less scripted would also be beneficial.