There are multiple reasons why the US might be reluctant to provide Patriot missiles:

1) Their record in Saudi Arabia agaisnt Yemen hasn't been great. The US doesn't want to show weakness

2) There is a VERY limited number of missiles available. Having a launcher and no missiles doesn't really help Ukraine

3) The operators need extensive training to use the systems well. That is time Ukraine doesn't have.

4) Up to 70% of weapons shipped to Ukraine don't make it to the front. Sending Patriot missiles increases massively the chance that Russia can buy one on the black market and then analyze it for weaknesses.

Your numbers on casualities for Russia are impossibly high. 75 soldiers a day is 22,000 in Bakhmut alone. That corresponds to the equaly impossibly high numbers for 100,000 dead Russians in 10 months. Where are photos? We saw immediately the stalled Russian convoy towards Kyiv in March. Day after day after day. We saw images of individual bodies in Bucha. Day after day after day. If there were really (avg.) 75 dead Russians every day in /around Bakhmut, there would be a steady stream of media material. Day after day after day. The fact that there is not - and I've looked - says to me it doesn't exist. I could be wrong, but this doesn't fit the pattern of western reporting.