Avery would be best suited to be the pitbull defender off the bench to harass a tired starter or outplay a backup.
C's need a SG that's a genuine offensive threat in order to be competitive
So Memphis started TA, and I believe they were competitive. OKC started Sefolosha and they were also competitive.
Sefolosha is a very good 3 point shooter, and an efficient offensive player overall (with low volume, but that's probably more a function of playing with KD and Westbrook). He's also big enough to guard any SG in the league.
Tony Allen is more limited offensively but still more effective than Bradley, and also has the size to cover anyone.
That said, I think Bradley has the potential to be a starter - just not next to Rondo. I think Bradley paired with Steph Curry or Kyrie Irving - bigger PGs who are good offensively - would be great.
That might have been slam's point - that the Celtics in particular need an offensive-minded SG because we have more of a pass-first PG who's no threat from 3 point distance, and who doesn't himself have the size to regularly cover SGs if Bradley is taking the PG (which is when he's most disruptive).
I agree with you though that if Bradley develops a reliable corner 3 (36-38% from there would be good enough I think), he can play a bigger role. Combine that with his baseline cutting speed and I think you have a useful offensive player.
I'm no expert but his form seems fine, and he has had stretches of good shooting before. There's hope.