I think it depends on the couple. Some couples keep their finances seperate and some don't, and some continue to do so after having DC's.
DH and I keep everything seperate. All the bills come out of one account (a joint account), and 50% of this amount is debited from each of our private accounts every month. We also have another joint account into which our holiday savings go, and an equal amount from each of our private accounts go into this. Since we earn roughly the same, we're left with about the same in each of our private accounts to spend each month. We each do an equal amount of housework (we actually do it together at the same time, which is kinda sweet... i'll dust and he'll hoover, i'll do the dishes and he'll wash the clothes, he'll mow the lawn and cut the trees and i'll sort the flower beds, etc).
Some couples continue to work this way when the woman has children, and as you describe some couples have it so that the woman has to dip into her savings to keep up her side of the arrangement. Personally, i do not think this is fair.
For a start, giving birth and doing all that stuff is a job IMO... and it's a job that's as necessary as your DH earning money to pay for the electricity and water, children don't look after themselves. As such, i think it is fairer for him to pick up the financial slack whilst you do the unpaid work. Now i understand that his wage litterally won't cover your expenses by itself, but i don't see why it has to be your own personal savings that pick up the slack, he should have savings to contribute too (or else he should start saving!).
I don't have children, but when i do have them DH and I have agreed that i will take a year off. During this time, i will not contribute financially at all. Instead, the housework will not longer be split 50/50... i will do all of it (except cooking the evening meal, because he has a passion for cooking and wants to continue doing it), and i will look after DC. Of course, he'll also look after DC when he gets home because he loves the idea of being a father, and i bet he'll continue to do a fair chunk of the housework because he's very kind and will probably want to see me relax. :)
So my opinion is that splitting the bills 50/50 is a great way of working, but one one of you stops or reduces work to have children and take care of the house then it is the responsibilty of the other to pick up the financial slack. I don't think it would be right to continue to pay the bills 50/50 if one of you is doing more housework or looking after the children more.