I've had one "normal" eye and one very nearsighted eye all my life, and was not patched as a child. Consequently, my brain divides the labor automatically, assigning distant vision to my left eye and reading and other close tasks to my right eye. Now that I'm in my 70's, I find that I need reading glasses for sheet music on a music stand - which is too close for my distance eye and too far for my near eye - but all my friends have to wear reading glasses too, so it's no big deal. (I actually remove the lens from the right side, because it just confuses my right eye, which had no intention of reading the music in the first place.)
So it's not necessarily true that the weaker eye will lose any function - it may develop its own specialty, as mine did.
The one disadvantage I have found is that I don't have true depth perception. 3-D movies, stereoscopes, and binoculars don't work for me, and it took me a while to understand why I'm so poor at playing tennis or catching a fly ball. Parallel parking is even worse for me than for other people.
But I'm here to tell you that if mismatched eyes aren't perfectly corrected, it's not the end of the world.