The way I understand it, miners add transactions to the blockchain in exchange for a fee and for newly minted coins. The rate of newly minted coins was determined by the early adopters of bitcoin and cannot be changed unless 51% of the miners decide to fork the blockchain.
If this is correct, then in theory, a cryptocurrency can be made with the inflation rate determined by the number of transactions included in a new block. If many people adopted this currency, it would achieve transaction speeds far greater than any other cryptocurrency.
I believe that such a currency, made for fast trading rather than holding value, could be a good complement to Bitcoin. It isn't feasible to buy a cup of coffee with bitcoin and wait see to confirmations of the transaction before you drink the coffee -- however, this would be entirely possible with Fastcoin.
One of the problems with quick blocks is more chances of forks and orphaned blocks. The quicker the blocks are discovered, the more chances there are for parts of the network to be out of sync with other parts of the network.