Do we think that Bitcoin mixers/tumblers will become useless as blockchain analysis gets better?
I think the opposite. I think mixers, tumblers, coinjoins, and other privacy enhancing techniques will both continue to be developed and improved upon, and will also become more and more in demand as blockchain analysis companies, centralized exchanges, governments, and many other third parties spy ever more heavily on bitcoin users.
Will we create applications that analyze the blockchain well enough to see through mixed Bitcoin?
Many of the mixers which use the "classical" technique of sending coins to a deposit address, the mixer bouncing them around with other users' coins, and then sending some other coins back after a delay, have already been broken to various degrees. There is a great document discussing this here:
Breaking Mixing Services. This is why it is important to use a reputable mixer which cannot be broken in this manner and not just any old mixer you stumble across.
