The problem with this is that Bitcoin is just about the least anonymous thing ever. It only seems anonymous because nobody's built the infrastructure to track it yet.
This statement is a bit hyperbolic. Bitcoin isn't as anonymous as say cash, but it's a lot more anonymous than most online payment methods (excluding a few altcoins which can really just be seen as innovations in the bitcoin/blockchain space).
Bitcoin will evolve to be exactly as fungible as is required to maintain its efficiency. As the cats build tracking tools, the mice will continue to expand on bitcoin's fungibility.