All you're doing there is replacing one arbitrary version identifier with another arbitrary version identifier. People would still know what browser you're running because we'd quickly see "rainbow tables" with UUIDs and the browsers they correspond too. So the problem you're attempting to solve would still exist.
I think you're underestimating peoples ability to waste time writing lengthy bad solutions which follow a behavior they're already familiar with, rather than properly researching a good solution.
Again, you can't fix everyone. If someone is dead set on doing useragent sniffing, they are going to do it. No technical solution is going to stop them.
But by changing how the useragent works I think we can get rid of the vast majority who only do useragent sniffing because it's the "easy way out", it's the quick fix that will let them get back to development instead of fixing a bug or shimming a feature.