when I first heard about the many-worlds interpretation it was in the "popular" version about the universe "splitting" on the random events meaning one copy of the observer would see one outcome, and another copy the other outcome. However, later I've read several other accounts that completely discards this view and says that MWI is really just a "relative state" interpretation describing the interaction of wave-functions of the system and the measurement apparatus/observer etc. In this way it does away with the seeming "branching" of the universes. However, my question is then: How do these relative state interpretations then explain the fact that humans never observe systems that are in "superpositions" - all human experience involve precise outcomes. The splitting-version of MWI seems to better address this since in this interpretation each "copy" will see only one particular outcome, but with the relative state formulation this doesn't seem to be handled - humans will still exist in superpositions themselves which doesn't explain the human experience of definite outcomes?
The Quantum Mechanics interpretations, such as the many-worlds-hypothesis, are all structured to answer the question of how we could observe classical deterministic behavior even though experimental evidence suggests that there are quantum behaviors which defy classical deterministic behavior. They all start from the assumption that what a human being perceives with its senses is exactly defined by classical laws of physics.
They key to all of this is an assertion you make: "all human experience involve precise outcomes." This assertion, while natural, is remarkably hard to prove. In fact, a highly preferred modern interpretation is that this assertion is actually false. Instead, the assertion is replaced with a statistical one: "all human experience is statistically indistinguishable from precise outcomes."
NeuroFuzzy wrote the answer into a comment. The reality is that, if you look at experiments that are traditionally considered to be "classical," you can model their results just as well using quantum mechanics. However, when you do this, you typically assume that the billions of states in your sample are "decoherent," that is to say that they can be well approximated by random variables with little to no correlation. When you do this, and apply the central limit theorem, you find that most of the quantum effects disappear under a pile of statistics (due to averaging), and the remaining effects can easily be lumped together into "classical" laws. As it turns out, one must be very careful in constructing their experiment to cause the correlation terms to be sufficiently strong as to be observed as "quantum effects."
This same thinking can be applied to your eye... its behavior can be governed by quantum mechanics. The same can go for your brain -- its behavior can be governed by quantum mechanics. In general, they operate in regions where the quantum effects are small, so we can approximate them very well with classical mechanics.
However, this does not sit well with some people. Somewhere in the brain is the mind and consciousness. Many do not like the idea that the mind may be governed by quantum effects at all. And so, many of the hypotheses posit that there exists some classical observer to observe the world (and quite often that observer is the human mind). If a classical observer does indeed exist, then the interpretations (such as MWI) are needed.
However, if a classical observer does not exist, then the interpretations are less essential. If the things we consider to be classical observers (such as ourselves) are really only merely "statistically well modeled as a classical observer," then we can instead model everything using quantum mechanics, and recognize the points where the coherent effects of quantum mechanics play so little of a part in the signal that we can simplify our model and just use the classical approximations.
Of course, it's also possible that quantum mechanics is just an approximation as well. We're still improving the theories as we go; nobody knows what we'll find next!