To begin with, show me a GP that works part time and qualifies for any means tested benefit. Most 'part time' GPs are actually working 35-40 hours a week, because they do paperwork and admin, in time when they are not meant to be working or are working very long days, perforce.
But that's not what I said. I said that someone on £100k loses their personal tax allowance, so automatically becomes £12.5k worse off when they cross that threshold. After that, they are taxed at 45%. So I think it's something like £150k that is necessary before they break even and take home more than they were earning at £100k. To mitigate that, many go part-time, and/or pay excess into their pension schemes, which are not taxed. This means that the treasury is not getting the higher rate taxes anyway, so what is the point?
The child benefit thing is the same. Someone on £49k gets it, but someone on £50 doesn't, so that person loses £40 a week, or £2080 pa (tax free) straight away. They are also taxed more on every pound over £50k they earn, so have a long way to go to break even on the extra hours or promotion that took them over that means-test threshold.
I also didn't say that pensions are benefits. Pension credit is, however, and lots of people who are on that did not pay NI contributions, (or not enough). I am fully aware that one generation pays for the next - which is why I described it as a ponzi scheme - but at the time contributions are being made people are paying for education, health, defence etc for everyone, so freeing up money to be spent on pensions so it balances out. Reciprocity. When people don't contribute they are essentially getting a free ride on all of that, and younger people are paying for those who never contributed (reciprocally) before they got to pension age. I didn't blame pensioners either - I specifically blamed the system!
I also said that many people are better off working in the long term, but I would need to see evidence of at what point that becomes true for those who work part-time and get top ups (subtly different from benefits), which is what I was talking about. If you earn £10 and get another £10 in UC (obviously made-up figures) then you have £20. If you work full-time for the same £20 (or even £25) and have to pay childcare out of that (plus more for for bus fare and other work-related expenses) you are worse off, and not seeing your children as much as someone getting the top-ups. Why would you do it? Yes, your pension and promotion prospects are enhanced, but that benefits those in professional work far more than someone on minimum wage and a zero-hours contract, and not everyone can look to the future because they are too busy staying afloat in the here and now.
My figures are all rounded up or down, so are for illustration only, as I am not an expert, but I'm pretty sure the principle holds.