I am glad that Trek abandoned the different badges for other ships. I never did care for it. I am glad that the symbol for the Enterprise was used for all of Starfleet.
It is cool though to see this one close up!
My understanding is that the different patches represented different divisions or sectors within Starfleet. That's why we see the delta shield at the starbase in "Court Martial" because that base was in the same division as the Enterprise operated within. The other Starships operated in different divisions of Starfleet; hence the different patches. Ultimately the delta shield was adopted for the entire starfleet after the Enterprise was the only starship to survive the 5 year mission in tact. Don't know how accepted that is but it is my understanding.