Why did Starfleet stop assigning each Starship or Starbase their own. The Exeter, Constellation, Defiant all had different assignment patches different to that of TOS Enterprise. Even the Colombia had a different patch than Enterprise. But now all of them use the same Delta for all the ships. Why the Change?
They were not supposed to. It was a production error according to one memo from the TOS production. So, there was the Command insignia (flag officers, starbase personal), fleet personnel (the Enterprise delta) and merchant service (The Antares). I know that a lot of fan ideas was that the delta was adopted to acknowledge the Enterprise's successful completion of the 5 year mission. But, from a BTS perspective, individual ships were not automatically supposed to have their own.
https://www.startrek.com/article/starfleet-insignia-explained Read this article, goes into detail about creator intent and production errors (the Exeter). The Defiant was correctly given the Delta in TOS, but when they brought the ship back for Mirror Universe episodes they gave her a unique insignia because they were operating under the same assumption fans had for many years.
What we get is what we get, though. So fan rationalizations are the ultimate word on the issue! We just need to consider not just what we have so far, but also what we might get in the future, so our rationalizations won't backfire. Are individual patches and symbols going to make a comeback? Probably not in any "future" production, because Star Trek has abandoned the practice long ago and isn't comfortable with it. But with "past", "prequel" productions, the creators are likely to be well versed in Trek lore, and it's fashionable to milk the lore (regardless of franchise, but especially in scifi) for fancy details, of which these patches might be one. Truly ship-specific patches in ENT would be a United Earth Starfleet thing, a bridge between now and Trek, and not a "problem" or an "issue". What we have in TOS is an anomaly we need to explain away, though, since the arrowhead rules supreme in UFP Starfleet in general, and also in modern flashbacks to days during and before TOS. "Ship-specific" doesn't really cut it to begin with, since some of the TOS badges spanned more than just a single ship already. But we might go for "Fleet-specific", now that Trek post DS9 acknowledges the idea that Starfleet would feature many distinct Fleets; perhaps our cameras have always been pointed at the First Fleet, except for a couple of times in TOS*? The other way to go is to plead different branches of the service, but that sounds a bit hollow when two of our unique patches come from sister ships to the hero ship. In the end, our "ultimate word" is fairly unlikely to get challenged. But at least one of the spinoffs under works, Strange New Worlds, is going to try and exploit the TOS niche of storytelling. When we spot our first sister ship in that show, then we can tell... Timo Saloniemi * Kirk did seem awfully ill versed in what the sister ships were doing. Perhaps each Fleet would have one of those, and the Fleets don't share itineraries much?
In real life terms, marketability. The Starfleet arrowhead is iconic and everyone knows at a glance it represents Trek. So of course they're going to use it, with minor modifications to differentiate which version of Trek you're watching. Why doesn't Star Trek: Picard use the exact badge from "All Good Things" but a very close yet unique design instead? So they can sell badges of both.