Mojang has actually considered this exact suggestion in a "combat snapshot" (note that 6 hunger is equivalent to 3 full hunger bars, each of which is 2 hunger points):
Saturation boost removed
Eating food is now slower (40 ticks, was 32 ticks)
Natural healing works longer (down to 6 food points, used to be down to 18)
Natural healing is faster (every 3 seconds, was 4)
New: Natural healing now always drains food points. Saturation is not used when healing damage and is only relevant as a "pause" until food drains (as originally intended)
Sprinting is no longer affected by the food value
I'm not exactly sure what the second-to-last line means but it seems to say that saturation now has no play in healing; even if you have full saturation healing will drain hunger instead (this means that visible hunger will start decreasing immediately regardless of what you ate, but you don't have to eat again until you drop down to 3 hunger bars). The only thing I do not like at all is the slower eating, but that's why mods and older versions exist (I'd much rather be able to spend less time eating at the cost of slower regeneration, not that I'd ever actually play in such an update, just as I haven't since 1.7).
I don't think they need to remove Saturation. It adds a little mechanical complexity and depth. I do think they need to make it more plainly visible, though, so you're not having to guess what your Saturation is.
I don't actually like the combat test system which splits healing from saturation and just makes it drain food directly. It seems very annoying, especially if you're like me and frequently break your ankles because I spend a lot of time building and, inevitably, falling, that'll really just jack up the amount of food I need to carry and eat. It's more inconvenient and removes some room for depth, so I don't support.