I think that it's important to differentiate between privacy and anonymity.

Anonymity is when people will not know who initiated a transaction. This is how monero, dash etc works. But this is not really enough. If a government agency wants info about who made which transaction, they can always find the IP that the user initiated the transaction from. BAM it's over.

Privacy is when you have both anonymity and your location is kept private. This is achieved when using coins that operate over the TOR network like Deeponion and Spectre. These are the coins that will rocket when people finds out how vulnerable monero/dash is.