1) Why would it be prohibitively expensive? In the face of severe enough penalties, most people would simply report their transactions as required, and report who they transacted with.

The number of transactions that needed to be investigated would be a small percentage of the total, and possibly traceable through means other than cracking keys.

2) Regardless of whatever zCash is, my point is that Bitcoin's immutable and complete ledger lends itself to complete surveillance. The math may be uncrackable, but the users are not, and privacy would go out the window if they're forced to transact with registered IDs.