What do you mean it is "centralized"? It does rely on specific servers, since it does not download the entire blockchain.
Yep, that's what I mean. From what I understand, multibit also does not download the entire blockchain and is able to function without relying on centralized servers.
Is it possible to have the best of both worlds? Meaning security/privacy through changing addresses, backing up only one private key or seed, and not relying on somebody's servers?
That already exists... Bitcoin Core.... Multibit... They already have those features.
If you consider nodes as servers, then no, that is impossible.