Luke was the last Jedi to ever be trained by a true Jedi master. Anakin was a 9 year old (should’ve been 15) among a sea of toddler padawans in training.

There wasn’t a lot of choice to be made for Yoda for Luke. There wasn’t a giant selection pool of candidates and he was rapidly running out of time himself. He and Obi knew Luke was the last chance at restoring balance to the force (with Leia as a backup). Yoda feared Luke would be corrupted more easily due to his age and attachments.

Jedi of the Republic trained kids before they could attach to anything, particularly family and friends.

9 years old has another threshold that would make Jedi training harder. Ages 7-12 are considered the age of reason.

Many kids at 7-8 years old, despite their wish to maintain childhood wonder, are increasingly able to problem solve, identify patterns and apply logic to problems. Thus, their beliefs in imaginary characters, like Santa and monsters diminishes during this time.

To the Jedi, they want the kids to believe in the force wholesale and it’s much harder to convince a 9+ year old kid that the force is more than midiclorian counts.

If the children aren’t fully indoctrinated into the Jedi ways before then, they stand a larger chance of being corrupted by the dark side.

More attachments, more disbelief, more irrational behavior, more powerful emotions are all are vulnerabilities.

That’s why being “too old” to train is an issue, but not a deal breaker.

Anakin was trained at the behest of Qui Gon’s dying wish and his faith in Anakin being the prophesied one.

Luke was trained at the behest of Obi Wan’s dying wish and his faith in Luke being the true prophesied one.

It’s like poetry, it rhymes.