I don't think having an H1B helps you accelerate your citizenship application in anyway, and for many countries the wait for legal citizenship is decades long.
Except this is literally false. Every single study I’ve seen that claims this has no real evidence - just speculation without knowing the details of the jobs or the people being hired, based on their own self-serving false comparisons to make dubious claims that similar jobs are paid differently.
Since you said “across the board”, do you think Google or Amazon pay a software engineer at the starting level differently based on immigration status? No, they don’t. Literally every manager at big tech could tell you this confidently.