Time Mage is Godlike even without Reset hype - still has overkill damage off 2x Meteor, just not quite as overkilly.
Mechanicswise, I lean toward allowing Reset, albeit with a "player frustration" limit that nixes using Reset more than 4-5 times to get perfect results. That said I'd have little objection to disallowing it in the Dungeon for power/flavor reasons. The situations where Reset can backfire are very specific and not all that common. It's quite a huge power boost. As noted Bartz is a 4.0 so maybe that kind of power is okay, but FWIW, when I was thinking of making a Time-travel themed Stocke / Crono team for awhile, I would have requested a custom synergy Sealstone which was basically a one-shot of this ability, albeit not tied to the survival of any particular character (you lose? Okay try the fight again from the top.) It's quite solid if you have any unreliable statusers on your team (Jean as noted), and it's good even against opposing hax. For example, it means that enemies who want to turn off the Reset spigot are 100% required to go kill / Silence Bartz before anyone else, which may not always be possible (some enemies don't have critical rates, or must do something really suboptimal to threaten a Bartz kill), and even when it is possible that makes Bartz basically a pseudo-Firefly holder, which as we know is always good.