I think it is a good strategy to target carers of the most vulnerable as the ability for the NHS to send carers out to assist has been compromised by Covid.
Indeed with the need for the most vulnerable to shield pretty much the only way they are likely to catch it is via those family who look after them round the clock.
I was a full time carer for many years to my mum who was fully bed bound after a massive stroke so needed 24/7 care. That's why I got a free flu jab 20 years ago when too young to otherwise qualify. If she was still alive I would certainly have been expecting for her to get priority given her vulnerability and I would have had to take her there if they could not come to her and risk catching it when out too so it would have been wrong not to do both at once just for an extra dose.
I am sure common sense is being applied on personal circumstances that local GPs will know about, of course. and this is a factor in making decisions over prioritising. And who to vaccinate alongside the most vulnerable.