Then you are comfortable making a decision that could cost thousands of lives over one with a few hundred without taking in any other information other than a radar bounce that is approximately the same size/speed.
I mean you're largely correct. What I'm saying is that there may be a standing order to destroy all ballistic threats, and to exercise a very high degree of caution (high level approvals for each engagement) with any potential air breathing / subsonic threats. I imagine this is a common order given to Patriot batteries in hot, but not war, areas.
BTW, this is a bit similar to why the US very clearly advertises the Tomahawk as not nuclear capable - so that a few subsonic blips do not trigger a strategic exchange. The Russians do not do that, many of their commonly used missiles are dual purpose.
The Tomahawk was deployed with nuclear warheads, in several variants, between 1983–2010 or 2013 [0]. As far as I can tell, only the ground-launched variants were consistently advertised as non-nuclear, and that was to comply with the bilateral treaty obligations of the INF [1]—and there was a ground-launched nuclear Tomahawk, too [2], which was destroyed in 1991 when the INF treaty came into effect.
I don't think that there was ever a *unilateral* US aversion to these things. We've fielded large numbers [3] of nuclear-warhead cruise missiles—air-, sea-, and ground-launched, spanning much of the Cold war. We're currently developing a new one right now [4].
Ugh, I was clearly wrong about the Tomahawk, and I don't know why I thought so. It's probably not a believable story for the adversary, so such self-inhibition cannot yield any strategic results anyways.