I would rather suffer 5-10% fraud if 100% of the eligible recipients are able to receive the benefits.

With the current system, far fewer than 100% of the people intended to benefit will actually make the cut.

There’s no reason to assume it would be as low as 10% without strict checks. It could easily be 90% or more. We already see big regional difference for tax and medical fraud which likely reflects different enforcement levels and knowledge about how to skirt them.

But you're not going to get 5-10% fraud. Already there is significant disability fraud way past your 1% number even in our strict system. e.g. there are counties in the US where almost 1 in 5 working age adults is on disability because they are supposedly too disabled to work.

Most people won't commit fraud in an honest system, but that flips rapidly when they see fraud being tolerated. You make it easy to defraud the program and the fraudsters will pile in. Your staff will be overwhelmed and 90% of the applications will be fraudulent. Just look at what happened with the PPP program during covid. It's estimated that $200 billion was lost to fraud.