We've always had 1 parent full time and 1 parent part time as it shows the children that you work to earn luxuries, but parental responsibility is important we personally think an adult should be there before/after school. That is just how we rock, not saying it's 'the' way.
The children know that Dad now pays for bills and a few treats. If you want an app or some tokens on the QT that comes out of Mum's bank.
On the benefits side I can give you a direct comparison. Two families split up same year, both families have kids stay with Dad. One family the Dad works full time, the other family claim benefits. Even though Dad has a trade he can easily fit round childcare.
Fast forward 20 years, Dad 1 got made redundant and found another job before he had to leave long term job, both kids working. Dad 2 is still on benefits and none of the kids are working. Even if we fast forward 30/40 years Dad 2 will still be on benefits albeit a different one now, as they've got a bit hardcore with JSA I believe.
I'm proud to come from Dad 1, it always shocked me that Dad 2 just was not arsed in showing his kids that in order to exist, you should get a bloody job. Another comparison I started working as soon as it was legal, because I was bought up with - if you want you earn. The other person reached 35 I believe never having done a job, same with siblings. I lost contact a few years back so not sure what's going on now.
Obviously it was one of them friendships where you share mutual interests, so if you wanted to share the excitement you would pay for the other person. Shockingly it quickly mounts up.
I even said oh do work experience alongside me, it'll give you skills to put on your CV. Not you won't get paid but the plus side is you don't have only factory work as an option. That was a bad idea, the person was laziness personified. I'd hit print, busy office, 15 minutes later the person would drag themselves to the printer, 'It's not there!' Press print again, basically repeat the process till you have to get off your arse and see what the fuck was happening. Not only that sitting next to you with a magazine or journal work paid for, feet on my desk, I'm learning so can't help or pay any interest today.
I think I got my first grey hair whilst trying to do the person a favour. My boss loved it as I was management gold, but when you've got a sort of friendship, management goes out the window. At drinks with colleagues there would be a laugh and joke about it, so I could unwind. Then the other person decided she wanted in on it. We'd go to a really nice wine bar where the managers would pick up a round each. Everytime she would eye up that list, I swear she just looked at the price.
I do have a story I tell but I can't as it'd out me. But I was in hospital, I helped this old lady who struggled a bit, she wanted to introduce me to her daughter. It turned out said person was working with the daughter, but the daughter would go down the back stairs to avoid conversation. It felt so good to know it wasn't just me. The daughter was like it'd be great if you could do an exhibition for local kids, as they had guests come and do that. I just couldn't face it. I do feel guilty as the old lady took a liking to me, so did the daughter, so it could have been a good friendship. They were banking on me going to this place to see bump into them.
But the moral of my super long story is working breeds morals & a work ethic into your kids and makes 9/10 want to achieve. My Dad didn't have it easy, there were no top up benefits then, we had to be pretty creative with food. My siblings and I took on housework, cooking for each other, we weren't the Waltons as we wanted to kill each other, but still we worked as a team for my Dad.