Although Yoda made the same point with him.

Further, one could argue that he did have those same exact issues, despite an almost "best" case scenario at the time Yoda brought it up, as it relates to this issue: the only family he knew was killed on the farm, his best friend from his past life was killed in the Death Star battle, his mentor and teacher was killed escaping from the death star, and he had no idea who his father really was or that his sister even existed.

The only major attachments he'd formed that could still be used against him and his training were those he'd made to his friends, and to a lesser extent, his cause.

And what happened?

As soon as his powers were trained to the point that he could reach out with his feelings and sense (and be sensed) across the wider galaxy, literally as soon as he gets to that level, the Sith use it as a weapon, and manipulate him using his few attachments, lure him away from his training and out of hiding and indeed directly to Vader, who then puts another barb of attachment into him by revealing his ancestry.

Had Vader not had the dual "failure" of both trying to recruit his son against the emperor and then later turning on the emperor (and of course, Palpatine's arrogance in underestimating both Luke's resolve and Vader's attachment), the plan would have absolutely worked, dooming the Jedi and the Alliance in one fell swoop.

Like...not only is Luke not a great case for "age doesn't matter", he's very nearly the poster child for why it does.