>There are a lot more limitations and checks on what the US can do

If only those "limitations and checks" were actually followed by the US government and intelligence agencies. Here are some examples I collected during a previous discussion of US vs China surveillance states

https://www.aclu.org/issues/national-security/privacy-and-su...

https://theintercept.com/2018/06/25/att-internet-nsa-spy-hub...

http://thefreethoughtproject.com/national-id-hr4760-biometri...

https://www.theverge.com/2018/1/26/16932350/ice-immigration-...

https://theintercept.com/2018/01/19/voice-recognition-techno...

https://www.zdnet.com/article/us-cell-carriers-selling-acces...

https://theintercept.com/2018/06/25/att-internet-nsa-spy-hub...

https://freedom.press/news/revealed-justice-depts-secret-rul...

https://www.eff.org/nsa-spying

https://www.eff.org/cases/first-unitarian-church-los-angeles...

https://www.eff.org/cases/jewel

https://www.eff.org/cases/hepting

https://www.eff.org/cases/smith-v-obama

https://apnews.com/d69a8e6db867477795f4152d0511bbf9

https://www.reuters.com/article/us-usa-security-records-fact...

>Because there not beyond imprisoning or killing people over information gained

The US government also certainly uses the information gained to kill and/or imprison people, although you could perhaps argue that the scale is not the same

https://www.pbs.org/wgbh/frontline/article/inside-the-cias-k...

https://www.theguardian.com/us-news/ng-interactive/2017/oct/...

https://www.washingtonpost.com/?utm_term=.dc5b7bd3682e

>we have no reason to believe the US had implemented backdoors in major processors.

There is evidence that US intelligence agencies have backdoored products in the past. Personally, that's reason enough to believe that they may have backdoored processors as well

https://arstechnica.com/tech-policy/2014/05/photos-of-an-nsa...

https://www.infoworld.com/article/2608141/snowden--the-nsa-p...

https://www.technologyreview.com/s/519661/nsas-own-hardware-...