As for the Fed actually providing more money directly to the people (thus avoiding the "borrowed money" problem), there are two problems with that.
One is that the U.S. is such a large country that providing cash directly to people quickly, at a personal level, is impractical - and that is why, when the government wanted to provide some cash to people during the downturn a couple of years ago, it did so for most people by having the I.R.S. deposit it in people's bank accounts using the auto-deposit information they provided on their tax return for getting their tax refund (which didn't do the government any good anyway - the people were supposed to spend it to help jump-start the economy, but most people are cash-poor and saved it instead, since they were so very insecure during what were very uncertain times for most people). Yes, some people got checks in the mail (they didn't have to file a tax return or didn't get a tax refund or, at least, did not provide the information to get it electronically) - but to do a check for everyone would have been an enormous undertaking administratively (just printing all the checks would have been an enormous task, and quite costly).
The other problem is that the law against recessions is, more specifically, a law calling for full employment at low inflation - and was passed in 1978, a time of high unemployment and rising consumer price inflation (and could then not be enforced right away because consumer price inflation took off more than either the government or the Fed bargained for and so they had to deal with that first, which, for the time being, meant a choice between fighting high inflation and fighting high unemployment - but see this website, at the My model link, for why this was inherent to the Kondratieff wave at that point in the cycle anyway). The Federal Reserve is tasked, in effect, with maintaining a perfect economy indefinitely - and the law specifically calls for low inflation because consumer price inflation was high when it was passed (but I call it a law against recessions for convenience because of the era when it was passed - I lived through the 1970's, I remember well what that decade was like).
So what is the most basic issue in central banking? Don't flood the economy with cash - avoid a hyperinflation!
So there is no way the central bank is going to be willing to risk pumping too much cash into the economy - and is therefore quite content to pump new money into the economy through the banks, which is a (much) more convenient way of doing it anyway in a modern, fully-computerized society.
But there is a flaw in that thinking - namely, that they think they can keep doing that forever (i.e., loan defaults won't eventually skyrocket) because they believe they can avoid recessions forever, which implies keeping an economy going forever (their underlying assumption is that they can do that). But the Kondratieff wave puts the lie to that - and that is why I was able to predict the downturn of 2008-2009 in the summer of 2001 already (when I found out about the law against recessions). I also predicted the slowness of the recovery coming out of that downturn - because I know that an economy will slow down over the course of time, which means resource utilization also goes down, which makes the recoveries slower and slower. And wages also stagnate toward the end - which is also happening (unlike in a hyperinflation - a wage and price spiral to, effectively, infinity). So loan defaults have been going up. All the conditions that I would expect to see these days, per my model, are in place - and they point to deflation, not inflation (which will be evident once people cut back on their spending enough so that prices start coming down). The Fed is supposed to avoid both high inflation and deflation - so they won't pump the economy full of cash because they want to avoid high inflation - but they won't ultimately be able to avoid deflation because it is an inherent part of the final phase of the Kondratieff wave. The Fed has not been able to avoid the other parts of the Kondratieff wave - those have played themselves out, with some of them stretched out over (in some cases much) more time than usual because of all the manipulation by the Fed - and the Fed will not be able to avoid the tail-end either, in fact, that tail-end is building more and more, inevitably and inexorably.