You can do this, but it has consequences. Money is not inherently valuable. It's a medium we use to store and exchange value inherent to scarce goods and services which people demand. To be a stable representation of value, money must also be scarce. This is a fundamental concept of economy, not something decided on and enforced by government.

The money a government gives to citizens must come from somewhere. They could liquidate assets owned by the government, borrow it from another government, take it from entities who are subject to the government's authority (taxes), or - what I assume you're getting at - just make more of it.

That last one isn't as simple as it sounds because it doesn't increase the cumulative value of the currency. Printing dollars is like dividing a pizza into more and more slices. It doesn't increase the amount of pizza. Inflation is a very real problem that has annihilated economies.

Funny how none of that ever comes up when we're discussing bailing out corporations. Quantitative easing by itself was several trillions of dollars arbitrarily invented, let alone the various bank and corporate bailouts over the past decade. And don't forget that we literally allow banks and such to print money and stocks on demand (aka leverage) to allow them to make money.

In any case, value fiat money is not a product of rarity, it is a statement of the value of future tax receipts. Money encodes/is an exchange marker for work done or promises of work to be done.

It does come up with regards to bailouts. There are tons of people who are opposed to corporate bailouts and who worry about inflation and a ton of problems created by the zero interest rate policy etc.