Though it was retconned in, Mr. Miyagi never used the pressure points himself, and as demonstrated by Johnny in Cobra Kai, it's not exactly Hokuto Shinken.
He's also never thrown anyone through a wall, the best he's done is use Terry Silver's own momentum to throw him into a mirror.
The arrow-timing is neat, but I don't think it gels with the rest of his combat feats consistently.
Just to address this, he did break fallen support beam during the Okinawan storm, but I'm presuming the log is this one:
He doesn't break it. It's a symbol of the past friendship he had with Sato he spends the movie trying to rekindle. Even as a display of supriority, that would be pretty cruel if he did.