This is definitely something interesting.... however, it is not important at all. Bitcoin doesn't need anonymity. Those who need it have things to hide...
that's naïve. people automatically have it when using fiat. if you were using bitcoin for everything you'd pretty soon be longing for some anonymity.
in a full bitcoin world everyone would know what you were earning, what you spent things on, what you paid for things. you might start off pseudo anonymous but one slip up could link your id to all of your addresses.
businesses would have their finances wide open for other businesses to analyse. there are ways to cover your tracks right now but they're not foolproof and i don't reckon people should have to put conscious effort into something so important.
Some Bitcoin users need anonymity, and some don't. That's why mixer companies make profits. In a full Bitcoin world nobody buying stuff like a coffee or a McDonald's would care about anonymity, like when they pay for those things with debit cards today. For transactions where people care about anonymity there's already mixers, and there would still be mixers in a full Bitcoin world.