I come from the future, bearing important news!

Probably the easiest way to show that Ha'ro's suggestion requires additional postulates is to use a toy model like a weighted quantum coinflip. Because flipping a coin is nice and simple, the extra step required to eliminate states of low amplitude squared really stands out. If you do a single flip, you get probabilities of 1/2 from counting states, even if the amplitudes squared are, say, 0.4 and 0.6. If you flip many independent coins, you should just be able to multiply the results together, which means counting states still gives the wrong answer - if something else supposedly happens, that's a property called "nonlinearity," which normal quantum mechanics provably does not have.

This can be quickly seen if you spend a lot of time on this stuff, which is why nobody has gotten a paper published about it specifically (though there are plenty of speculations about changing quantum mechanics to be nonlinear). Yhis is a case where no journal articles specifically on something doesn't mean it's "not investigated" - it just means no articles.