What math and data did you use?
If we want to show this is a general mechanism and not specific to bacteria the problem gets much worse with slower generation times and more complex protein functions.
I’m not seeing any problem.
Here are some data:
https://www.jbc.org/action/showFullTableHTML?isHtml=true&tableId=tblII&pii=S0021-9258(19)51632-5
So how do you define a “single function” given data like these?

This is less than one per gene over 30 years and is after 50000 generations.
If you think fixation is relevant to search, you don’t understand what those words mean.
Exactly.