This setup makes me feel deeply uncomfortable - I think there's an underlying sense of women being inferior and financial control/abuse.
I have an East Asian background, and this concept of pooling is alien to me. I know someone said it was common in both South Asia and East Asia, but I've never come across it before.
With that said, we believe that the higher earners, no matter who they are (male or female), should support the rest of the family if they are able to, not because they have to, but because they want to. We all look after each other as much as we can based on the different circumstances/stages of life.
For example, my parents put me through university by making huge financial sacrifices at the time so that I could focus on my degree. Now that they are retired, and I am working in a good job, I send them money each month.
There's a sense of intergenerational support, but the difference is I don't have access to my parents' bank accounts, and they don't have access to mine. We all retain independence and dignity. As long as everyone is sensible (and it's a family trait), there's no need to ask where the money has gone. We certainly wouldn't tell each other how to spend our money.
By not merrily sharing cards and PINs, we're not putting anyone at financial risk of the bank refusing to pay out if there was fraud by a third party. I shudder to read of you openly saying you share financial details with people who aren't cardholders - do you know what a huge risk you are taking? Or have I misread, and everyone is an additional authorised cardholder with their own PIN?
I wouldn't expect a partner to give my parents money or for me to give his parents money, only for him to respect my wish to support my parents out of my own income. He could do the same for his own if they needed it, and he was so inclined.
The way that I do finances, I think, has a similar outcome to what you are trying to achieve, OP, but in a way that doesn't put any of my family at risk. It also doesn't involve taking money away from children.
I hate the idea of taking money off kids because the patriarch said so. I don't think it's a healthy attitude to teach in the UK, and it puts them at risk of being seriously taken advantage of by other people. (Well, as well as by their father.) If I knew someone took money off their kids, I wouldn't give anything to the kids that was cash or could be easily turned into cash.