Too lazy to search for the exact link but I seem to remember reading some editorial in the financial section of The Economist about 3-4 months ago where they were saying that bonds are sort of cash-like, or were sort of cash-like when that article was written and when the papers on which that article was based had been written. If that premise were to hold true (even in part, meaning bonds are sort-of-cash), maybe most of the "rules" economists have written down until now when it comes to the cash vs. bonds relationship would need to be re-written.
For the matter, I don't take much of what it's written down in The Economist at face-value anymore but their financial stuff is still pretty spot on.
(I'm a couple months behind and working my way forward, I just read this a couple days ago)
Yes. But that cash has to come from somewhere. If there's less cash in the system in aggregate, those with it gain leverage. Which means they can get a higher rate. Which raises rates.
The leaky bit in this equation are banks. They can magic money out of nothing to lend against a bond. The patch to the problem is capital requirements.
When the Fed sells a bond, it's taking cash out of the system and exchanging it for a bond. In monetary terms, it's destroying cash. That's tightening. When the Treasury issues a bond, it swaps it for cash. Same as the Fed.
Whether the Treasury or the Fed sells a bond, it has the same monetary effect. The difference is the Treasury's issuance is twinned to public spending, making the net effect neutral. (When the Treasury spends it creates cash.) In the short term, however, when spending precedes issuance (or vice versa), the gross effects can be real.