Fractional reserve banking would not be possible without taxation because the money would be worthless

Bank credit is valuable only because of the deposit guarantee. The deposit guarantee makes it valuable because then if the Government is to refuse it in the payment of taxes, it will be being a hypocrite.

The deposit guarantee makes bank credit valuable because it makes it suitable for the payment of taxes, without the Government and taxation bank credit would be worth nothing, as with fiat cash. Bank credit is valuable only because of the Government and taxation, it is a suitable substitute for cash because of the guarantee. It is the combination of taxation and the deposit guarantee that makes bank credit worth more than nothing.