“The problem is that Rav Kanievsky’s position is contrary to what the common practice seems to be.”
I doubt it’s really all that common, a frum Yid should rarely find himself in a situation when it’s nearing time to daven without his hat/jacket. Even if it is a common situation (and I can’t say I’ve seen that it is), then it’s still not an IDEAL situation.
“It’s near Mincha time and you don’t have a hat/jacket. There is no time to get your hat/jacket and still make the minyan. So, what do you do? Do you daven alone or do you make the minyan?”
Why are you out without your hat/jacket? If you don’t wear them all day long, then did you forget you would have to daven mincha? Ok so, it sounds like a one-off situation, in which case you could accept not making the minyan which would have the added advantage of ensuring you are in hat/jacket the next day.
The problem seems to be that most who aren’t in Jacket/Hat haven’t simply “forgotten” them, they daven without and “feel” it to be acceptable. It’s not something to police, certainly, but if it was myself I would have serious misgivings over casting aside the words of the MB and R’ Kanievsky with nothing to back up my “rogue” stance.