If I have got this right, years ago, people could either collect their pension weekly in cash from a Post Office, or they could have it paid into a bank account and possibly to a Building Society account four-weekly in arrears. So to go from collecting to into a bank account meant going without State Pension income for several weeks.
Then the government wanted to try to reduce money being paid out in cash at Post Offices. I don't know why, perhaps to avoid the fees to pay for that to be done, but quite possibly to avoid quite large tranches of cash being delivered to, and at, small, vulnerable, village Post Ofices across the country.
So perhaps offering direct payment to a bank account every week was the only realistic way to achieve that wthout causing cash flow problems for many elderly people.
Though I suppose that they could have made it that all new pensioners got it to a bank accounr four weekly in arrears.
I was quite surprised to get the offer. I had envisaged a strange sort of effect of money from the State Pension arriving every four weeks and money from my occupational pension arriving every calendar month, so sometimes both at about the same time and some a fortnight or so apart and at various short and long gaps between them as time went by.