Critics argue that the agency’s work with a lobbying group is a conflict of interest.
Then these critics don't understand the relationship between state and capitalism, because it is in fact serves both parties interests quite well, by design.
The state doesn't exist for the benefit of society.
You do realise that many people (significantly more since covid in fact) are on benefits because we can't work, right? And it's those benefits (disability, employment support) that are getting the worst cuts.
So you're not technically wrong, but your solution also doesn't help those of us most targeted.