Yes the size of the blockchain is fast becoming a problem, especially now that enthusiasm about Bitcoins is growing much faster than the technological means to store the blockchain. Also, the size of every block is going to grow explosively as soon as online services everywhere start accepting bitcoins as payment option, and THAt will be much more problematic.
But then, it'll just drive some more division of labor, with people storing the blockchain and verifying transactions getting paid for the service, much like what is happening now in the mining part. There will definitely be growing pains and I can foresee a near-term future where transactions get a LONG time to validate because miners are swamped with transaction volume.
As for your suggestion, it cannot apply to Bitcoin in any way or shape. Reducing the size of the blockchain means making a "summary" of it where all the wallets that are now zero get short-circuited in the transaction history. i.e 'wallet A sends 1 BTC to wallet B which then sends it to wallet C', you shorten it as 'Wallet A sends 1 BTC to wallet C'. But that eschews the hashing process entirely, so it cannot be done trustfully AFAIK.
Can I just ask your opinion, how does this protect someone who buys into Bitcoin from it actually being a Ponzi scheme?