Two problems with that.
As far as I'm aware the state pension is paid by those working. When they retire those then working pay for the pension of those who have retired. So when I was working I paid for the pensions of those who were retired. Admittedly it would have cost more if there hadn't been frozen pensions at that time, but times change. Sometimes people move to be with adult children who look after them, not always through choice. Times change, and so should the state pension. You'll notice they don't mind changing the age you receive the state pension despite what you thought was the retirement age when you were working.
Also, I'm retired and I pay tax on all my pensions and on the rent I recurve for the flat I rent out. I pay VAT on fees to the letting agent and any other costs related to it. The only income I don't pay tax on is on foreign income which is zero.
Just recently the PM said the government should look after those who had worked hard for their retirement. He didn't say it depended on where you decided to doyen your retirement.