Apart from the cost of means testing, it seems a lot of people in need don't apply for the money they're due for various reasons including pride and presumably competence. Some things are very fundamental needs and the state's right to make those automatic/ non-means tested - the reality is, for whatever reasons, lots of people would suffer if they didn't.
Apparently in 2016 'analysis of last year’s Department for Work and Pensions by Church Action on Poverty revealed that between them, working age families and pensioners are failing to claim more than £10bn a year in benefits. Others suggest low income households are missing out on £15bn in benefits and tax credits.'
https://www.independent.co.uk/money/spe ... 85166.html