Not if the escrow is an ecash mint or a market of agents. And sure, you can adopt it for those technical reasons, and that is the free market at work, but in the long-run I think it won't hold as a reliable currency for reasons not just tied to privacy. In the future, Monero will probably be utilized as just an intermediate swapping currency (which ecash mints can already act as and in my opinion will evebtually supercede the usage of Monero), but even in that case people don't want to hold it, they want to get rid of it. Cash is a perfect comparison: I use it because it's more private than my credit card, but I don't want to hold it. This is most obviously evident with the XMR/BTC price chart. I'm not arguing that Bitcoin is better at privacy with this point (though, there are ways to make it more private), just that it is better money.