So ... about Jerry Maguire

At the beginning of the story Jerry is “great at friendships but terrible at intimacy.”

Eighty percent of the way through the movie, when Dorothy/Zellwegger leaves him, he’s still terrible at intimacy.

Then Rod/Cuba Gooding comes within an eyelash of a very serious injury, and all of a sudden Jerry is not afraid of intimacy anymore.

What did I miss? What caused the change in him?

Jerry Maguire is an interesting movie because the ‘turning point’ happens right at the start of the movie where Jerry realises what is wrong, writes a mission statement and then executes that mission statement through a series of hits and misses we call life.

Yes! Well stated. The Mission Statement is what set him in a new direction.

He was mocked for it by his coworker cynics who predicted (correctly) that it would get him fired, but it was what he needed to write when he wrote it, and he lived a better life after that because of it.

But how did Rod’s near-injury get him over the hump of fearing intimacy?

IIRC, he observed the way Rod’s wife reacted on the phone with him when she witnessed the injury on TV, and understood that this kind of caring is something you only get when you have that emotional intimacy like Rod and his wife do, and felt what he was missing by keeping himself distant.

Rods acting up for the crowd (“dancing”) is what allowed Rod to be loved by the crowd and offered a decent contract finally. It was a great day for his near-broke agent Jerry, but when Jerry looked around him at the success he found he had no one to share this experience. He missed his wife.
That and just straight up loyalty is a HUGE theme of this movie.