It seems potentially detrimental to the flow and core enjoyment of battle, if it's a turn based or active JRPG. I love strategy as much as the next person, but if characters run out of endurance too fast, forcing a rest period, it could be a hindrance to play.
Personally, I like the idea of a status meter. Over and above just having status effects like poison, you could make the TP meter represent a character's overall health and well being. Keep fighting, walking on certain terrains, their status meter will drop. You could create new status effects just for this, like infection, fever, other diseases and perhaps enchantments.
Characters can eat actual food to restore the meter, as well as rest properly. This would add a layer of caring for your party and characters over and above driving HP potions into them between battles. It could also give a crafting feature like cooking a real purpose in supplying TP restores, whilst keeping any potions for HP & MP you may have planned.
I'm seeing it even as a way to potentially characterize, now. You could tune each character's resistances to diseases and medical conditions, based on their species, ethnicity, geography, etc.
The more I think about this ^ the more I want to use it myself.
This could allow you to really define the concept of Hit Point vs Health Points, making HP represent Armour durability and wound severity. Perhaps it's even possible to make it so that, when HP hits 0, you don't die, you just go critical, and all further attacks come out of your TP until death.
I would put in a secret accessory equip:
The IV Bag. Casts regen on your TP meter, so you never have to stop trashing ass until all your allies have gone comatose.
I think your endurance idea can work too. Only tweak I might suggest is giving a tiny restore at the end of, or start of each battle. Only a few points, but just enough to prevent the feature from making battle seem complicated and undesirable.