The problem here isn't a lack of training or culture. Properly "washing your hands" takes a surprisingly large amount of time. In practice people don't do it not because they don't know how or don't want to but because they can't. They simply don't have the time either in general or sometimes in a specific situation.

If you want to make a significant impact here, you would need to hire more staff.

Don't US hospitals do that the NHS in the uk is fanatical about it

I honestly don't know what is typical. There are things like this (I went and searched it up, I have dim recall of other discussions of the culture not embracing the lists):

https://www.advisory.com/daily-briefing/2015/01/16/jama-why-...