Anakin’s Lightsaber

Ben: Your father wanted you to have this when you were old enough, but your uncle wouldn’t allow it…..

Was this all bull? Or have they ever discussed Anakin telling Ben that if he did have a kid(s) he would want him/her to have his lightsaber? This sounds like something that could be idle conversation while nesting with Gundarks but Obi Wan have just scoffed at the idea of him having a kid .  And Anakin kept losing the blasted thing so there will be nothing to give.
And besides Jedi aren’t supposed to have kids. So it’s not a Jedi tradition to pass down a lightsaber like an heirloom.

How irresponsible if it were.  What if the child wasn’t force sensitive? Don’t give a non force user a lightsaber. Unless you’re an ex stormtrooper or a scruffy looking nerf herder you couldn’t even use one.