It would seem to complicate the problem of having lightweight mobile clients. The private keys will have to be explicitly and completely shared with the server in order to even search for transactions belonging to the client.
Correct. That's the tradeoff for anonymous transfers.
Also, if bitcoin gets as big as they want to speculate, very few people will even be able to run full nodes, and some of the nodes will serve huge numbers of people. It's not a matter of having 20 local accounts, but a matter of having 20 million accounts that are explicitly searched.
It is a tradeoff. Perhaps the best solution is to support both methods, and my version can be used only (or primarily) for cases where you need to broadcast a receiving address.