That’s not true, in some cases.
I manage a recruitment business. We employ staff for schools.
There some roles that we cannot fill without using overseas candidates.
Invigilation - it pays minimum wage, it’s only hourly pay, and it’s sometimes 2/3hrs depending on the exam length. It’s seasonal, so not worth hanging around all year for, and the work is at best tedious.
Personal care - low paid, but still not as low as doing it directly with a school. Short hours, up to a max of 20 per week, right in the middle of the day. Also not always the most pleasant work either.
On an average week we have 20+ personal care assistants, in one location that we cover. During peak seasons, we can need up to 30 invigilators. I can promise you, because I’ve spent 10 years trying, British people won’t do that work to the volume that is needed.
Schools can’t find them themselves, the education system is so knackered that they don’t have the budget to pay more for lower skilled work, and we can’t fill it without overseas support.
Without those people, the examination function in this country wouldn’t work, and there would be disabled children not adequately cared for. I can see the real world positive impact of migration in my area of work every day.