Canon is what's on screen. Period.
Whether it's any good or not, is up to the individual viewer.
Here's another way of looking at it. Canon in the Biblical sense carries the concept of "Is it real?" "Am I supposed to believe this?"
That's one of the reasons why "canon" is so tied into "consistency." What parts of what they have shown me am I to accept as the "real history" of Star Trek?
"Am I supposed to believe that a group of grade school kids can run a starship?"
"Am I supposed to believe that Spock has a never-ending supply of siblings, waiting in the wings for a story which can use them?"
Those types of things are up for debate, but I think a significant number of people would like to see that debate based on something like the merit of the story or how the story progressed characters. Instead, the debate frequently centers around the equivalent of "Gene decided he didn't like all the work that he got paid for in TAS, so he also decided none of it was canon," or "the Voyager producers were so embarrassed by one episode that they declared it null and void." Those types of arguments, which come down to "We fucked up" don't really help anything make any kind of decision.
Ultimately, everyone creates their own canon, hence the term "head canon". At this point, I am of the opinion that each series takes place in its own universe, and some episodes do as well. That's an easy way to cut out the crap and not have to deal with making it all fit. It doesn't have to fit, and when it doesn't fit it's two different universes you're looking at. I can't help but notice, though, that the MCU fits together pretty darned well, much better than Trek, across dozens of products. I have to believe that Trek could have done that if the will was there...or maybe the talent...but it wasn't. Pity.