Going by one interpretation of time travel/temporal progression, everything and everyone that "was" quietly removed from existence (by whatever means) has already been removed; nobody missed anything because there was never anything to miss. While you process that implication, enjoy your mini-migraine.
Reminds me of some time travel story I once heard about, that played with that trope.
Set in a universe where time travel was possible, the two protagonists of the story take a walk through their neighborhood. A bench in a park catches the eye of one of them and he asks the other if he thinks there's anything suspicious about it. "What do you mean", the other replies, "that bench has been here for the last 25 years... there's nothing out of order". The other, slightly exasperated: "Yes, I know that bench has been there for the last 25 years ....but was that the case yesterday, too?"
I hold to a difference between in- and out-of-universe perspecive. For example, we have the original (TOS) timeline, that was then altered by the events in First Contact, resulting in an alternate timeline (Enterprise, Discovery, etc). For them, as in-universe, obviously, that always has been the timeline. It was never different to them; the original TOS timeline never existed. But for me, as an out-of-universe-observer, the original timeline was, and probably always will remain, what we see in TOS.