If they allowed a bunch of teens with Superboy-like powers to join, nobody could ever defeat them.

They should...furthermore, they should be able to recruit from any era they like...so you could have a young Diana Prince or a young J'onn J'onzz (for example) join them for adventures sometimes.

They've done that at various times--Superboy and Supergirl were both members,as were Mon-El and Andromeda,and Lighting Lad and his sister Lighting Lass when she had electrical powers.

My theory is that that "rule" was a guideline for the writers more so than for the LSH members themselves.

Well, they let Triplicate Girl stay after she became Duo Damsel. Although that might have been a case of an existing member being grandmothered in.

Of course, that seems like a ridiculous rule.

Still… because of that rule, I did get to enjoy the first appearance story of Wildfire (then called ERG-1),
which had him showcase that he could duplicate all of the Legion's power set. Then he gets rejected
because he won't demonstrate his "one unique power" that he has above and beyond those others.

But yeah, even while reading and enjoying that one, the kid in me was pretty much screaming "Why would
you turn down someone like this? Fools."

It would be fun to do a story where a team of would-be heroes who never bothered to apply
to the Legion because of duplicate powers were recruited by some evil organization, which
uses them to utterly demolish the Legion.

The Legion of Super Mercenaries? The Anti-Legion? I love that concept.

There's a story that's kinda sorta like that ...

Actually, I guess it's pretty different. Never mind.

Legion of Super-Villians?

Geoff Johns and Gary Frank in their Superman run did a story where the villains were people who applied to the Legion and were rejected. (Which probably has been done before, now that I think of it.) But that's not quite the same as not bothering to apply, plus they weren't rejected because of their powers.

Still, the story itself was freakin' awesome.