Not quite. There would be two scores: Proficiency bonus, and zero. Whenever you pick up a d20, you are either going to add your proficiency bonus to the roll, or use the result straight-up*.Now that is pie in the sky!
But in seriousness, can you explain everything being "folded into a single proficiency?" Wouldn't that make everything the same score, no matter what you are doing?
This would have a number of benefits. It would all but eliminate one of the biggest sources of confusion I have seen at the table over thirty-five years of playing D&D: Which number do I use for what? Likewise, it virtually eliminates character sheet math. And it would make skills, attacks, and saving throws fully independent of each other, allowing for a greater variety of concepts without sacrificing effectiveness. Do you want to be a fighter who's also an intelligent and learned scholar? No problem. You no longer have to wrench points out of the stats that are vital to your survival (Strength and Con) to invest in Intelligence. Just take the Sage background, put skill proficiencies in Arcana and History, and the rest is roleplaying.
Now, to what would be lost: You'd have a lot less granularity (none, in fact) in measuring how good you are at X versus Y. I don't think most players care much about that, but some folks care a whole lot. There is also @Steampunkette's excellent point that we lose the ability to represent certain things mechanically; the hulking barbarian and the scrawny wizard now have the same encumbrance limit, and Legolas and Gimli have no reason to wear different types of armor. To address this, I would use a feat-like mechanic, where you can choose traits like Powerful Build (double your encumbrance) or Evasive (boost your AC when wearing light or no armor). The key is that these traits are binary--you have them or you don't--and they don't affect anything else. The barbarian who doesn't take Powerful Build is no less effective at hacking up monsters.
The other thing that would be lost, however, is fifty years of D&D tradition--it would ignite a backlash that would make 4E look well-received--and that's why this is pie in the sky.

*In practice, it wouldn't be quite that simple. Stuff like Expertise would have to be accounted for somehow; though I might replace Expertise with a Reliable Talent-type mechanic, where a floor gets put under the roll.
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