Positron to replace proton as the nucleus of an atom

I know that the positron and electron have the same mass, which allows them to annihilate, and I know how solve the 2 body Schrodinger for a standard hydrogen atom to get the orbitals.



My question is why the math works out the way it does. Is there an "intuitive" (I use that word cautiously) quantum mechanical explanation as to why the masses have to be the same in order to annihilate and why the electron will keep its distance if the nucleus' mass is different? Why don't the proton and electron annihilate and just produce enough radiation to make up for the differences in mass/energy?



Thanks