Requiring new addresses to avoid the quantum computing threat is really on the 10-50 year security timeline from my limited understanding. New addresses while maintaining old addresses is what Mt Gox does, there are probably better and worse ways to do it. A set deposit address is going to probably be safe, Seals with Clubs the biggest bitcoin poker site seems to favor set addresses, people tend to keep these fairly private anyway.
We'll leave it as a single address for now. For increased privacy, a customer can order takeout rather than delivery, and then pick up their pizza or convenience store items discretely.
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Cool, the theoretical threat that makes reusing addresses potentially undesirable is only to a small degree an anonymity threat. The big threat would be finding a shortcut to compute private keys for addresses known to hold substantial values back to their private key. The sort of power to pull this off is a long way off though, and before that happens another address scheme using a still more secure scheme could rather trivially be added to bitcoin.