No, ability to issue a controlled lot of physical currency is the meaningful differentiator, which is why the relation to banks is irrelevant.

I can buy $1 worth of Bitcoin, declare it ErikCoin, acceptable only in my stores at a 1/1,000,000 denomination, and I instantly "minted" $1,000,000 in cryptocurrency, using only the Bitcoin blockchain.

Bitcoin doesn't let people be banks, it let's people be the mint.