I would expect transactions to simply become expensive.

Then, people would go through trusted third parties (e.g. online wallets) for small transfers, and only use the blockchain for large transfers.

The small transfers would just be adding or subtracting "virtual" bitcoins between different users' accounts.

Clearly, such a system would optionally allow for fractional reserve banking.

I view bitcoin more as "digital gold" than "digital cash," for the above reasons.