Some will be in private rentals where housing benefit is significantly insufficient to pay the rental charges. So the money needed for living expenses instead has to be used to pay that shortfall first and keep a roof over their heads.
Only after that expense do bills, food and everything else need to be budgeted out of what remains.
Whereas, exactly the same family in a property with rent covered by the LHA rate housing benefit, will be able to use the entire sum to meet their living expenses.
Every year my private rent increases, LHA rates take time to catch up. There is usually a £3/400 shortfall of housing benefit where I live. That is a lot of money taken from the other benefits actually needed to live.