How often does the delta show up in ENT? We can't call TOS the outlier if ENT also doesn't have the unified delta emblem.
I don't think the delta showed up at all on Enterprise. There was no insignia really, just the shoulder patch that listed the ship name and a picture. I just happened to catch that the Columbia patch was different from the Enterprise patch.
My guess is when they created the uniforms for Enterprise they wanted to strike a balance between current uniforms for NASA and later Starfleet uniforms. They are more utilitarian. And each ship had it's own unique shoulder patches probably to reflect that the original series showed different insignias for different ships. That held up until TMP. I always assumed before Star Trek (2009) came out that they settled on the Enterprise insignia by TWOK as a unifying insignia because it was the most successful ship in the Starfleet line and one of the few Constitution class starships that seemed to survive its mission unscathed. And Kirk and co. are arguably the best of the best. I think some of the novels ran with that idea as well.
Unfortunately when Star Trek (2009) came out they blew that all out of the water by having the delta used for all of Starfleet, including on the Kelvin which at the beginning was still supposedly from the prime universe. And the same with Discovery as well. As a continuity nut I have to admit that does bug me a bit. I wish they had used different insignias for different ships as reflective of the pre-TWOK era. In some ways it might even make sense for that era in story as it would quickly help you identify which ship or starbase an officer or crewman is assigned to at a time when Starships were out of contact for long periods of time.
So I don't really think the original series was an outlier. Before Star Trek (2009) came out the insignias/patches were different from the creation of Starfleet until sometime before TWOK. That was reflective in both the original series AND Enterprise I would argue. Star Trek (2009) and Discovery are what caused the discrepancy now.