What will be interesting to see is how exchanges and businesses react to this, as well as governments. The only reason governments are allowing Bitcoin to stay legal, or even neutral, is due the fact that they think they have the means to control it with efforts such as chainanalysis. Once/if BTC reached a point of actual fungibility in which the costs of trying something like chainanalysis are bigger than simply outlawing it, that is what I would predict would happen (that governments outlaw it and go into a full front attack), which will only make other governments become tax havens for BTC holders. Ultimately the price would most likely be pushed upwards but there would be an awkward period of, once again, "Bitcoin is dead" all over mainstream media.
I think it is worth noting that chainanalysis is based on very weak heutistics.
The reality is there is nothing linking an address to another one. (taking to the extreme, even a transaction with one input and one output). And each steps those heuristics become weaker and weaker every step down the chain analysis.
I am afraid the "chainanalysis stuff" is nothing would hold in a serious trial.
By the way batch transactions (output aggregation) togheter with coinjoin (input + output aggregation) are the best practices to transact over the bitcoin protocol. The fact that these techniques aren't implemented in "basic" wallets is not relevant. Everyone should always transact this way for every of his transaction.