This isn't necessarily true; the independence of the Fed is much more important when we're talking about setting the price of money (and other areas like regulation but we'll ignore that for now).
I don't presume the price of money should be "set" (another word for manipulation).
The Fed's independence is largely irrelevant to its role as the government's deficit enabler, because the central bank will always provide as much as the government wants. It just makes sense to include this responsibility with all the others that the Fed manages, in the same way it makes sense for any other government agency to have authority over areas of similarity. As you correctly point out, Treasury could perform the same function.
So, without the Fed, Congress runs out of money and is forced to stop spending. With the Fed, endless supply of money. Hardly irrelevant.
The point though is what difference would it make?*
The difference is who decides where the money goes. Private bankers, or politicians. Not only does the Fed monetize government debt, but every single loan it makes to a private bank is monetized as well. So we have a private entity making private loans against the public's bottomless checkbook, using monetary inflation.
*Additionally, since you're so obsessed with currency devaluation, exactly what do you think happens to the confidence in, and value of currency if a country just prints more money to fund its deficits, without any obligation to later pay that money back? In essence, you're basically advocating a system that is more akin to, say, Zimbabwe than the US?
In truth, I am not advocating such a system. I only use it as an example to point out how preposterous it is to give a private entity the power to issue money. Politicians have and would abuse this power as well, but at least they are presumed to be transparent and accountable. I advocate a strong commodity standard (probably gold, or bi-metallic), which must be coupled with statutes that strictly limit the amount of money creation to zero. Any standard which intends to limit the issuance of money based solely on the idea that the currency is redeemable will fail, just like the gold standard failed in the roaring twenties.