I think ENT was already the reboot, caused by FC, which is why the TC was even happening and involving ENT to begin with - because they were the first butterfly. Then they found Borg tech, and diverted all the way to DISCO.
Problem is, First Contact and ENT were supposed to be part of whatever timeline all the other TV shows were a part of (e.g., ENT leads into the future that TOS happened in). There's plenty of evidence to support this as well; with the events of First Contact being noted to be a predestination paradox in "Relativity" (VOY), Star Trek Beyond referring to pre-Kelvin timeline stuff from ENT, not to mention that "Regeneration" (ENT) was specifically written to be not only a sequel to First Contact, but a prequel to "Q Who" (TNG) and the other Borg episodes. Besides, the only reason the idea gets entertained in the first place is explain why the modern shows tech looks fancier, which is needlessly complicated when we've seen the shows coexist TOS tech with others, strongly suggesting that the look is purely a design choice of the casing and interface.