TP only ever mattered in AoE. You couldn't ever run out of TP against a single target enemy, really. Not when using any class that's actually TP user. Red Mage could run out though.

And together with methods of recovering TP that numerous classes had, that means that TP was a non-issue in any party that knew what they're doing and was not lagging behind on gear.

With this change however there is a question how will weaponskills work. If they will use MP, we run into an issue of them simply running out of juice. That means that failures (aka deaths) will be that far more destructive to the parties chances.
However, there is an alternative. These skills no longer using any resources at all.

Maybe only the AoE skills like Overpower will use MP to still be limited. Maybe not even they will, with the developers embracing the fact that there is nothing wrong with people pulling from wall to wall and melting everything at once with an AoE barrage. Right now it was restricted to well-geared parties, while the poorly geared parties would run out of TP long before the enemies are dead. Especially if some members don't AoE for whatever ridiculous excuse they may have. That causes a huge, unnecessary gap between players that are lucky with party...and those that are unlucky. By removing the cost to weaponskill AoE's that disappears since even one AoE user will be able to speed up the fight noticeably.

Even now, if you properly manage your resources, casters are unlikely to run out of mana. So sustenance is reasonable to expect from non-casters as well, after all. I for one would be very much for this change if that was the case.