If by "take care of" you mean put downward pressure on European wages, then sure. Unrestricted remote competition would benefit 3rd world developers and the 1st world employers. But not the 1st world employee.
My assumption was that European devs are underpaid wrt USA and that their wages will go up as shortage of devs in USA forces them to pay up for European devs.
Your assumption forgot that remote applies to the entire world, not just the Europe. Have fun competing with team from <insert South American Country> who mirrors time zones more closely with the US.
If by "take care of" you mean put downward pressure on European wages, then sure. Unrestricted remote competition would benefit 3rd world developers and the 1st world employers. But not the 1st world employee.