The ILR debate really hits home how far Labour and the unions have drifted from their founding purpose. The main reason there's been a shortage of care workers is because the pay is too low, the work isn't respected, and it's no longer a structured career. Care homes just want minimum wage workers, and they don't care about ability or suitability just so long as they maximise their profit margins.
Labour and the unions should want to correct this, not least to restore dignity for the elderly. Personally I do not want to spend my dying days in a care home tended to by random untrained Africans who are just here to exploit the visa system. Labour should want the care sector to be a viable career and an adequately paid profession, but now wages are so low that you can make the same money working at McDonalds with none of the physical and emotional labour.
Propping the care sector up with low wage immigrant labour so private equity care homes can maximise their profits is more in line with a neoliberal hellscape than anything resembling a Labour run country.