The easy way out

Quite. If you want a truly stable money supply you have to eliminate not just checking/current accounts, but savings accounts too (M2), and also money market funds (M3), and go on to ban *everything* potentially substitutable for money. I'm not sure you'd have an economy left after you did that. And if you don't do that, keeping the monetary base fixed has no effect on the economy as a whole other than to annoy everyone.