I'm of this opinion; Square has a habit of just removing things because we deem them "pointless" or "annoying" (see TP, most positionals, most DoTs, tank stances) instead of thinking of how to make those systems engaging. Rather than removing the stats entirely, give me reason to want stats that aren't Crit/DHit.
Want to make Piety a stat that isn't entirely pointless? Give healers a second filler nuke with a higher MP cost and higher potency, now we not only give healers actual MP management in their damage kit, but Piety now indirectly gives extra damage via more casts of their higher damage nuke. I'd go even further with this and have most jobs use MP in some form, and remove the healer restriction on Piety, making it a universal stat that could affect your rotation in some meaningful way.
Want me to meld speed? Have the speed stat also affect other damage cooldowns so I don't get punished with drift because I wanted to go fast (there's a lot of other problems involved, like the strict 2 minute cooldowns and GCD alignment over those 2 minutes to ensure you get as much potency during those bursts).
Want Tenacity to have some meaning? Reducing the natural defensive power of the tanks and give Tenacity a boost in defence to make up for the loss in natural defence. Another option would just be to greatly increase auto and buster damage (and frequency of busters), but that would give roughly similar results. This would give Tenacity a little more meaning as both a prog stat and "insurance" stat. Ideally the change should be enough to reduce the amount of healing spells needed to keep a tank up so it could act as an indirect damage increase, but that would require a lot more changes to encounter design and healer kits.
The answer to the stat system being bad and pointless is to make them not bad and pointless. Easier said than done, but this game doesn't need more things removed, it needs more depth.