I'm not sure that either of those statements is true. It could be, in some situations in some countries. As a general statement? No, because most government borrowing is not borrowing from the central bank.
> And somehow price of the money is centrally managed.
Empirically, that has worked out rather well - far better than "centrally managed" would lead you to expect. In particular, it has dramatically cut the number of severe downturns (which used to occur whenever the price of money became too high).