Basically this idea existed more or less before in the form of the ill fated 'firstbits'; I consider this proposal to be ill-advised for the same reasons.
Addresses should generally not be reused. Reusing addresses harms the your security and privacy as well as the privacy of all Bitcoin users. Extensive address reuse contributes to systemic risks which endangers the system (what happens when RPG weilding ninjas show up at mining farms with demands to not mine transactions belonging to their enemies? If regular transactions are conducted in such a way as to make their enemies transactions indistinguishable we never need to find out).
I agree about privacy concern. But right now, we have no way of printing a payment destination on an unpowered and unconnected device (aka paper).
The exception is stealth addresses which I have great hope once we resolve the OP_RETURN problem.
What about publishing the stealth address on the blockchain instead of a Bitcoin Address ? This would solve your concern of privacy while still allowing to be remembered in a few words.
These short addresses are immediately subject to lookalike attacks-- a popular address is "wolf larceny tape butter" ... great, I go and create "golf larceny tape butter", "wolf larceny ape butter", "wolf larceny tape butler" and so on... I spam these clones out in various places or just trust human error to guide things along, and now I'm receiving funds from other people.
This is not the usage I am envisioning.
I don't want to use such address to be recognized. My use case is more between two persons wanting to exchange bitcoin without the need of a physical stuff that bear the address.
-"where to I pay your ?"
-"Pay me to : Red, Car, Building, Trigger"
For human recognition, encoding an address on an identicon is more appropriate. In fact, I'm also looking out how I can make an identicon safe from lookalike attacks.
Also, BIP39 lists are created by making it hard to confuse between two words. What is important in this case is not the string metric, but the "sound" metric of the words. Assuming words were wisely selected in bip39 dictionaries, we should be relatively safe.
One could not resolve these addresses without a copy of the entire blockchain or at least a forever growing unprunable database
Well, the only information that gives problems is the Transaction Index in the block.
If I can find another feature for identifying the address, a partial merkel tree would be enough for solving your issue about the need of having the whole blockchain.
The client would just rely on untrusted third party services (or by connecting to the bitcoin network) and just check that address given the words are correct.
This also requires a separate registration step, which reduces the scalability of the system due to additional overhead, and make it less instant gratification. You end up with something where you have to pay fees to establish an 'identity' just to receive funds to pay the fees with. Necessitating multiple use modes.
I don't want any registration needed, so I won't do that.