Its not that good. At best, its tremendously fanwanky, with a fair amount of unimportant side-plots to venture about (mainly the two escapees whose story leads nowhere).
I obviously don't agree.

It has a good story, and the main characters are good. Its not really "fanwanky". Outside of the scrapyard and Telos (neither of which I knew about when I first saw the episode), its not like its filled with references, and what it has works just as well if you have no idea they're references to anything.
Of course it counts. If Colin Baker is performing the role of the Sixth Doctor, it bears mentioning. And he did for Big Finish. And from the '80's Doctors' outputs on BF, his material, at least until early '10's, is simply stupendous. His run with Evelyn Smythe is better than anything on 80's Who telly output (with certain exceptions).
And the blue coat isn't even his permanent suit, so that shows your level of wilful ignorance.
He never wore a blue coat, and if you think so that's your choice but also a complete fabrication. I can show you his birth and his death on video, and guess what? No blue coat. Saying "Well, he took it off right before he died and put his old coat back on", which is BF's way of trying to fix their stupid costume issue, is pathetic (plus he had no adventures outside of what we saw, obviously). You might as well consider those terrible (based on clips I've seen online) "Stranger" videos Colin Baker did as canon, since he at least appeared on video playing something approaching The Doctor and it even had Nicola Bryant. As for the other stuff, 80s Doctor Who was mixed, but still better then BF. As someone who suffered through
The Marion Conspiracy,
The Spectre of Lanyon Moor and fucking
Bloodtide (if this was canon it would be the worst goddamn 6th Doctor story), I prefer Mel to the annoying, argumentative senior citizen schoolteacher.
ES wasn't the reason TSoLM or BT sucked (although she was the reason that TMC was barely listenable), but she didn't help. The only good thing related to 6th/ES stories is that I listened to the stories through an online subscription the Public Library has, so it was legal but BF didn't get a penny from me. I mean, they probably got money when I bought the Last Adventure physical release from Amazon, but I got that as a collector thing to look at mostly (although I did listen to the stories) and ES isn't in it anyway. I could listen to even more of BF's Doctor Who stories through that service, but I can also just go to fanfiction.net and probably get better stories that are just as legit.
Brought down? Get ahold of yourself. BF's story output didn't worsen any Doctor's reputation in the slightest.
Fanfiction can't bring down The Doctor's reputation. It can make some fans bring up stupid junk when discussing a Doctor, though. Like Blue coats and terrible companions.
Fine, then don't listen to his BF run. But contrary to your belief, Colin Baker's rather proud of his TV run, as well as his BF run. He just feels his take on the role wasn't as nearly refined as he wanted it to be. BF allowed him to flex his muscles and expand his characterization to where he wanted to take the role. Calling his output with BF names because you personally don't like them is your own business, but fans who have ventured to them, like myself, have experienced a fuller, more enjoyable and entertaining journey with Six than just two seasons on TV. And your last sentese just makes no sense - there's no "rivalry" between the BBC and BF but what you make. Your strange contempt for BF is virtually of your own making.
The only really good thing about BF's Doctor Who stuff is the fact that the Doctor actors are putting in good performances. The material is crappy fanfiction, but The Doctors (well the real ones, not someone like Briggs who gets paid to do the shittiest 9th Doctor impression I've heard in a paid product) put in good work from what I've heard. Colin Baker deserves more work then what he got. Even if the material is awful and noncanon, I don't think badly of him or any of the Doctors for taking the work. They can all be proud of their performances, even if the actual stories are trash.
The 6th Doctor's real run was cut short, but it was good. He had 10 actual stories. You can like other stuff, but its not a journey. The Doctor never did any of the things BF said. I get not wanting to acknowledge that. I don't like to think about how the old Star Wars expanded Universe isn't canon anymore. But you can like something without acting like its relevant to a franchise. I may hate BF, but I'd be less inclined to fight against it if some of its fans didn't treat it like Doctor Who gospel. Some guy found a way to take money from a niche audience and the BBC and many DW actors went along with it. Nothing wrong with that, as long as its not treated like anything but what it is.