> All Bitcoin wallets, for example, use servers because it's impossible to do Bitcoin light clients (at least, they haven't found a solution yet).

This is totally false. So called SPV clients have been available since 2011 I think. Where the hell did you get this information? Just curious.

Examples of lite bitcoin clients include (but not limited to) breadwallet, bitcoin wallet for android (Schildbach), multibit, bittiraha-walletd etc.