I don't know how your family shops, but even your proposed joint account isn't going to give you "accountability".
Let me explain. A check is written on the support account at the grocers. Who's going to monitor to make sure that all of the food purchased with that money is eaten by the kids? Do we have the food in the fridge & cupboard marked? Does meal preperation include keeping the kid food seperate from other people living in the house? Do the kids get a different color toilet paper, does the household get a different bottle of laudry detergent for them, requiring their clothes get washed seperately. Since we need to account to the penny, can't divide utilities just by using a percentage of the cost of the household, can we?
Another check is written to a department store & several items of clothing are purchased. I can see people seperating their purchases into two piles, the kids & the other items pile, with each of them paid out of seperate accounts. Still, the wiley CP looking to beat the system can sneak some of their own personal items into that kid pile, so looks like you'd need to be given all of the receipts to go through, to get a "fair" accounting to the penny & even then, are you sure that each pair of jeans & shoes on that reciept was for the kids?
Looks like no McDonalds for these kids, as they don't take checks. Rummage sale items? Not for those kids, cuz they usually don't take checks either. Yes, there was a time when my husband & I were poor enough that the majority of our children's clothes were bought at rummage sales.
What if the parents disagree about items purchased? Say, (s)he paid $150 for one pair of shoes for the kid. Mind you, the kid needs shoes, but $150 for a pair? They don't *need* shoes that expensive (there are some teens that would argue against that position). Is there to be any recourse for an expenditure like that, which went beyond true need, but went to the child none the less? Do we get the court involved to resolve this difference?
Accountabilty in the manner you seem to want would give the right to micro manage much of the life of one parent to the other parent. It's not a fix. It's just adding another layer & I think divorce lawyers would just love it.