This is a very tired response, reflecting a real lack of intellectual curiosity and actual engagement with the issues. You are refusing to recognise how the situation has changed.
That study you reference is from 2018, based on data from the 2016/17 financial year, and makes two key assumptions - that migrants will earn around the average UK earnings over the course of their lifetimes, and that they will arrive in the UK around the age of 25.
Those assumptions might have been reasonable back then, but we live in a very different world now. Boris’s reforms to the immigration system, allowing in hundreds of thousands of poorly paid care workers (with no age limit - many are in their forties and fifties), slashing the income requirements for skilled worker visas from £30k to £25,600, and introducing the graduate visa, has transformed our immigration system.
And the reason British people don’t want to work in care homes is that it is extremely difficult and often unpleasant work that is extremely poorly paid. That’s not laziness. If you can make minimum wage working in MacDonalds or working in a care home, why wouldn’t you choose MacDonalds? It’s a far easier job.
If the government was willing to stump up the cash to pay care workers just a little bit more, we would have no recruitment crisis. Instead, we’re undercutting their pay to import middle aged Nigerians, saddling ourselves with their care and health costs in the not so distant future. These poorly paid care workers will be eligible for ILR after 5 years, and at that point can access Universal Credit and social housing - which they’ll definitely be eligible for because they’re so poorly paid!
This is the typical short termist thinking that both Labour and the Tories are guilty of - taking on massive future costs to avoid stumping up just a little bit more cash in the short term.