Nope. Once you learn such simple magics, they have irreversibly taken up a spot in your soul prohibiting you from learning other such simple magics. While you might eventually learn every wizard's spell ever created, including the mighty wish, if you did not select mending in one of your few simple magic spots, such magic is forever beyond you.
...which is one of the biggest fails of 5e, IMO. They tried a more reasonable version of giving at-will cantrips without forbidding learning/preparing others back in an early playtest, but it must have been too complex, because it was dropped in the next packet.
I personally allow clerics and druids to prepare (using one of their spell preparations) additional cantrips, which they can then cast at-will like any other cantrip. I allow wizards to scribe additional cantrips into their spellbook and do the same thing. I allow bards and sorcerers to choose to replace a cantrip with another cantrip on level up instead of another spell. This is mostly to cure the insanity and allow occasional flexibility. In practice, it is going to be rare that you prepare another cantrip instead of a higher level spell, given the limited number of spells you can prepare, but it does mean that you can if you know you need it for some reason.
With those house rules, your permanently known cantrips then actually become how the rules describe them, "Repeated practice has fixed the spell in the caster’s mind and infused the caster with the magic needed to produce the effect over and over." It makes sense that you could only hold a certain amount of that permanent magic attached to well-practiced spells, and it even makes sense that you might not be able to change them, because you've burned them into your brain/soul through repeated use. But you can still use other such minor magics just like you can any other spell.