The end result will be anonymous criminals, and no privacy for anyone who follows the law.
So much this.
Sorry to keep quoting things from the same source (in 3 of my last 4 posts; I'll give it a rest now), but your thought reminded me of the 77th footnote in that essay:
This may be theoretically possible but practically difficult: it might be hard to accomplish for technically unsophisticated people. This is why it is said: When crypto is outlawed only outlaws will have crypto (or privacy, or security) (original attribution unknown).