Hmm...my take on this has been sort of split for a while. On the one hand, I've always had a problem with the fact every class is tied to TP. It limits what you can do mechanically with resources and resulting gameplay. You can't have anything like DK runes or WoW monk Chi units because the limiting factor is TP regeneration (a rule the devs have set for pretty much every melee job). You run the risk of trivializing TP if you were to lean more towards extra resources while still keeping TP.
On the other hand, removing TP could negatively affect a couple of things. Firstly would be BRDs. As much as I hate that they were given TP/MP regen as a gimmick, BRDs would essentially lose one ability from the change. Jobs like MNK wouldn't be affected by the removal of TP too much, but you'd need to redesign DRG and NIN around some new gameplay mechanic to act as their limiting factor. There's also the matter of cross-classing, though Invigorate no longer being mandatory can be seen as a good or bad thing.
It's a mess, simply put.
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Something I could suggest is creating a distinction between STR jobs and DEX jobs by splitting how TP works for each. PLD, WAR, DRG and DRK could work with TP being a resource you build and consume on stronger abilities. NIN, BRD, MCH (and RDM assuming it enters as a DPS) on the other hand would have TP working similarly to what we now have, as a pacing mechanism. The only issue I see with the former (outside of having to redesign WAR, PLD, DRG and DRK) is that this system clashes with combos unless we make the "main" combos free and anything outside of that cost TP.
I know I didn't mention MNK, and that's because I'd make it the exception and balance it around a brand new resource with even more emphasis on Greased Lightning.
You forgot to mention XI's TP system created a bias towards big damage classes and burst damage in general. That was yet another reason why people didn't like RDM melee or sub A-rank skill weapons: "you're feeding the mob TP".The thing that people do not realize about tp is that it worked both ways for the player and the mob, at least in XI, which added an extra element of challenge. Since I do not have any experience with 1.0, would I want a tp system like XI in the current game? No. Why? Because, in all honesty, XI was a niche game, so people liking the main stream aspect of this game like either wow or some wow clone which is very present in this game.