Case in point: Vietnam. uSA and allies lost between 1/3 and 1/2 lifes than the North. And the USA loses were small (60.000 in a total of 1.5 million deaths). But it was a total defeat of the USA because none of the strategic objectives were achieved.
Ukraine: strategic objectives are being an independent country with a fairly working democracy. Russia: conquer and create a puppet state in Ukraine and keep pressing west againt NATO countries.
In the end we should measure against that, not by body count. I don't like it either.
Also, please try to Vietnam. The US is very favorably perceived, more than China or Russia, although probably below European countries.
In the sense, the US lost the war, but won in the end, at a very steep price, of course
US is perceived more favourably than China because their war with China was more recent and they have active disputes with PRC threatening island territories in South China sea.
Moreover, US has massive influence in terms of their media and their brands, something which China still doesn't match. Same reason even South Korea has massive appeal in Vietnam.
And USA defeated the whole communist block using the same weapons. Also, don't dismiss tourism as a _weapon_: it's would be more effective to send millions of frienly tourists to Cuba than to embargoe them for decades.
But that's disgressing. Vietnam was only used as a sample of strategic millitary defeat albeit losing less people. I don't think anyone in the Whitehouse has planned the vietnamese frienship ahead.
This has nothing to do with US intervention. China is also a market economy, the US never won a war there.