Same statement can be made for every career step. If your pay did not change, would you do the work of E6 at an E3 wage?
If I am moving to a position where I deliver more value to the company, then I should be paid accordingly. We need to move off this work for free trope.
I think you're imagining a "work for free trope" (which exists, but definitely not for mid/senior/staff engineering levels) where there is not one. It's a thought exercise, and being overly pedantic about it is not helpful.
The point is that if the only reason you have to move into EM is the bigger paycheck, you're most likely going to be happier sticking with your IC role and having the slightly smaller paycheck but enjoying work a lot more.
Same statement can be made for every career step. If your pay did not change, would you do the work of E6 at an E3 wage? If I am moving to a position where I deliver more value to the company, then I should be paid accordingly. We need to move off this work for free trope.