When the Fed creates new base money, that IS the savings of individuals and companies. It's their savings being involuntarily diluted away by an increase in the base money supply. 

If the Fed disappeared, the Treasury could issue debt, but what would it be denominated in? The dollar base settlement layer is an SQL database at the Fed, and the Federal Reserve Notes in people's pockets. Without the Fed, who's going to issue dollars? The Treasury would have to do it I guess, which would make the question obvious of why they bother with the charade of issuing debt in the first place. 

So the Fed can print within reason, but not really because they can't allow inflation? But if they do print it doesn't matter and has zero effect on the global economy and doesn't cause inflation? Can't quite square that circle personally. 

If it's just a number, why bother? Why not do what you suggest and let individuals buy the debt? At what price would they be willing to buy? 15%? 50%? 

When the Fed create smoney to buy Treasuries, by definition the money doesn't stay at the Fed. The Fed gets the debt, the Treasury (eventually) gets the money. And they spend every penny about as soon as they get it, so then it's in private hands, driving up prices.