OP, I agree, though lots on here won't. I'm in the UK so slightly different.
You can have a high earner bringing in £6k a month. Usually, on that sort of wage, you'd be working incredibly hard, long hours or doing a job that requires a specific skill set. When you've subtracted mortgage, childcare costs, bills, food, commuting (oftentimes, to London, which is also more expensive), fuel. You've also got one off costs: school trips, car repairs, insurance, dentist visits, prescriptions... you're really not left with loads of money. Some months it's difficult or impossible to save. People on that sort of income in the SE and London aren't living lavish lifestyles.
A single parent can bring in £3k per month with Universal Credit and working PT. Any child maintenance received isn't taken off or considered as part of the Universal Credit amount. If your child receives DLA you are exempt from the benefit cap and also get extra disability payments. Then you have all the subsidies; free NHS prescriptions, free school meals, free dentist, help towards winter bills, the recent cost of living payments. With all the subsidies, there can be instances where a single parent isn't actually too far off (income wise) what a high earner would be bringing in. I'm not saying this is the case for everyone on benefits by the way, but it is the reality for the few I know, and I'm sure many others.
I know all of this because I have friends from both scenarios.
It's clear why some high earners feel very resentful at being taxed so highly and there is little incentive for single parents to work more than PT and lose access to any help or subsidies.