Sure it is. Star Trek can and did tell a wide variety of stories using all sorts of styles. That was Gene's "vision", an anthology show with a permanent cast of characters. Action adventure is just as Star Trek as social commentary or any other style of storytelling. later it lost some of the anthology feel but was still willing to use a variety of story styles.You mean Hornblower in Space, like Gene pitched it? Or the "vision" of Trek that people came up with after it aired?Sells a lot of tickets but kind of destroys the original vision of Star Trek in the process.
Neither Gene's initial vision nor the composite that Trek eventually became nor what it became in the TNG era is what nuTrek is. It's none of the above. For some people, that's a good thing, and for others, it's not.