Realistically, immigrants who can't speak English would only get the lowest, most terrible jobs

You know what terrible jobs often are? Decently paying because its the only way to get someone willing to suffer construction, road work, and other shit shovelers. Places where there are no women, never were women, and women aren't relevant to any part of the equation because they are too dainty for such work. Otherwise its entry level work, which is a crucial piece of the equation for those of little/no experience (young adults) or people who just aren't worth any more than that. Those jobs serve a purpose beyond just "forgettable stuff I don't concern my privileged ass with."

Women are a bigger issue in soft work, like offices. Except even those are getting decimated by Indian immigrants too. Another completely independent factor effecting the equation.