When I say that monetary policy is fiscally irrelevant, I don’t mean that it’s conceptually impossible to raise a lot of money through seignorage. Under the current institutional setup, the demand for money is too small—if not for interest on reserves, base money would consist entirely of cash and a very small component of bank reserves—but you can imagine policies that would change this.
For instance, right now the only reserve requirement that banks face is the 10% requirement on checking accounts. We could expand this to, say, 50% on every kind of liquid financial balance, and demand for reserve deposits would increase enormously. Seignorage still wouldn’t balance the budget, but at least it would be a respectable contributor to annual revenue.
At a fundamental level, though, this is really just another kind of tax: the government requires that people who want to hold liquidity in the form of bank deposits also hold a government-issued asset that pays zero interest. And it’s a deeply inefficient tax at that: everyone would eventually find a way around it (so that it didn’t raise any revenue), but the accompanying process of financial innovation would be costly and disruptive. Even if the tax had no loopholes, it would be a questionable idea. When we can tax income or consumption, why tax a certain way of holding financial assets? (Some smart people have an answer to that question, though it probably wouldn’t involve the kind of massive tax I posit here.)
But regardless of the merits of such a measure, you can’t escape the fact that it’s just another name for a tax—and as such, there’s no need for it work through monetary policy at all. We could levy an explicit tax on banks and be done. Put that way, of course, the feds’ ability to raise money through monetary policy sounds less exciting: it’s just a disguised, relatively ineffective way of exercising the authority to tax. No special fixes here.