Another way to phrase my question: why doesn't conventional monetary policy include manipulation of long-term interest rates?
This question might sound "weird" at first glance, but please hear me out.
While the expectations hypothesis does not exactly hold, it is clear that through manipulating a series of short-term interest rates, central banks (CBs) are already impacting long-term interest rates. If so, why not directly influence it?
One may argue that it is prudent for the CB to not have long-term engagements --- as their interventions are primarily about dealing with liquidity crises (at least in the past) --- so they should only deal with short-term lending. There are at least two arguments against that. First, as long as the long-term bond is actively traded, CBs can also get out of long-term bonds quickly. Second, CBs today have fairly sticky reserves, etc, so their engagement is already not really short-term anymore.
I am sure there are good arguments for why CBs don't deal with long-term interest rates. At least there should be good historical arguments (even if they don't apply today anymore).