The argument against episodic television with a continuing cast is that the characters do not change at all. Star Trek can be viewed in any order with no effect to the characters--they are absolutely constant from one episode to the next. That's not real life where people change a little bit. That some--even most--serialized shows take character change to an unbelievable extreme is probably true. I can't say I find a lot of television compelling, and of most serialized programs this is no exception.
Again, you're confusing the extreme with the norm. That description applies to some episodic shows, but there are hundreds of episodic shows about which that is not true, such as ST:TNG, ST

The problem is that people today mistakenly equate "serialization" with "continuity," and therefore assume that "episodic" means "lacking continuity." As I've tried to explain, that's absolutely untrue. Episodic and serial are terms describing the structure of a story. Episodic shows tell a distinct story in each installment, while serialized shows tell only part of a story, sometimes multiple stories, in each installment. There is absolutely no reason why an episodic show can't have continuity from one self-contained story to the next, can't have characters remembering past experiences, growing and changing, having ongoing relationships, etc. And there is absolutely no reason why a show can't have episodic and serial elements at the same time. (Contrary to the abuse of the terminology in fandom, Babylon 5 was actually an episodic show, not a serial. It had an ongoing arc, but 2-parters aside, each installment told a self-contained piece of that greater whole, with a beginning, middle and end within the same hour. In order to be a serial, it would've had to have each plot spread out over several episodes. For instance, instead of there being a discrete episode called "Soul Hunter," the complete story about the Soul Hunter would've been spread out across multiple episodes along with other parallel storylines.)