ok, agree with you that once children are all in school full time, then unless there are health/disability issues, then there are very few reasons why a mother cannot work full time.
That goes for both single parents and those married/with a partner.
But, while full time working straight away may be the 'ideal', there are other aspects to consider. For instance, if a woman has been a sahm for a minimum of 5 years (be it on benefits or because their partners salary enables them to do so) then in the short term at least, part time working offers them the chance to ease themselves back into the world of employment, gain qualifications and experience, and help them to adjust to a new lifestyle change, before they go full time.
You could see the ability to do that as a luxury, but for many parents, going back to work is a daunting prospect, especially if it's the first time that they are leaving their children in childcare.
Your moral code is such that anything less than full time working is not good enough. Fair enough, you have high standards for yourself and that is actually something that I can admire and respect.
Nothing is always black and white though and sometimes you have to accept that other peoples way of thinking, while different to yours, is not necessarily wrong.
Tax credits, wrongly or rightly, are there to help people. If they were scrapped for anyone working less than full time, a lot of people would fall into abject poverty. They would end up on benefits like income support etc.