That's a misguided assumption that doesn’t hold up in practice because it assumes H-1B workers were "brought over" based on employer need for a domestic worker. The need isn't for a domestic worker, its for a skilled worker and the skilled workers want to work in the US because it yields higher compensation and opportunity.
Many H-1B workers request sponsorship from employers despite having the ability to work from local offices because they have in-demand skills that give the leverage to ask for it knowing that it will result in better opportunities.
Because H-1B workers had the ability to demand higher compensation via sponsorship and relocation to the US. Employers could say "no we won't sponsor you" but these workers are in demand due to their technical skills and could counter with "then I'll join another company that will".
If you remove the option for sponsorship then these workers will still be working their jobs because they're talented and in demand, they'll just be doing it from their home country instead for lower compensation.
Many H-1B workers request sponsorship from employers despite having the ability to work from local offices because they have in-demand skills that give the leverage to ask for it knowing that it will result in better opportunities.