Ahhh....no. Especially when we consider the leisurely four-year gap between Star Trek (2009) and Into Darkness, which is worse than the average wait between Star Wars movies when their up and running through a trilogy (and today's SW movies have shortened the gap, while ST is making us wait and wait...). I think the movies are fine as they are for the most part, and it's nice that there are some consistent narrative threads continuing between them.
One of the things that bugged me at the time (and bugs me even more in retrospect) was that Into Darkness was released four whole years after the first movie, but was only set a mere matter of.... months(?) later. It seemed to me that the actors were all ready to take the characters in new directions and show how they've grown in that time between films, but that the script and production were still in the orbit of the 2009 movie, trying to follow it up with a direct sequel and 'pulling back' on the character development to some degree. It's a bit like how The Motion Picture was made 10 years after TOS but tried to convince us it's only set two years later, it's like it stretches credibility a bit.
To me then, the first two movies do feel kind of serialized, like they're "Part 1" and "Part 2" of one story (the 'Abrams years', if you will), and that it wasn't really until Star Trek Beyond came along that I really felt we finally got a 'new' story that forged it's own path, unencumbered by being linked directly to the previous movie(s). And IMHO it was all the better for it.

