There's an old "I Love Lucy" episode in which the women and men each think the other's job is so easy. So, after a lot of dismissive talk and put-downs, they switch roles. And everything is an abject failure.
I think we use a lot of misleading and perhaps antiquated terms like "bread winner" and "provider" for (usually) men and "home maker" for women - when in a true team, both parties provide and both people make a home. And single parents certainly have to do both. It's all about what you value. So you're right, the term "provider" has a much broader meaning, and it should. If we truly value our families and each other, then we think that meeting all their needs and our own is important.
Any well-functioning machine is based on each part being just as valuable s the next, and we know they are all interconnected. From medical care to car maintenance to a good restaurant meal, it's only successful if each person does their job well. Families are the same.
There have been studies over the past decades (usually every time this whole argument pops up) about what the value is (or cost is) of services provided by the stay-at-home parent - we've all seen the analyses of what it costs for a cook, personal shopper, child care provider, health care manager, bookkeeper, chauffeur, travel agent, etc. The tragic way to work it out is when a SAHM dies and the single father has to pay for those services. The short-term way that a lot of people see it in action is when the SAH parent goes away for a weekend (without pre-cooking meals or doing all the laundry or leaving a list of where stuff is and who has to be at a team practice when). In fact, whenever a woman feels undervalued, I always suggest a weekend away without telling anyone how to do her job - when a paid person takes a day off from work, they usually have someone cross-trained already, right? So the same should apply in the home. (If the spouses work well together, then of course sharing info is sensible - I just mean when one person degrades the other one and doesn't value her role. Then stick it to him!)
Ideally, partners work this out before they have kids and re-negotiate along the way as things changes or as problems present themselves. I think the money can be discussed and worked out too. I think the money belongs to both partners equally (same as if one has a full-time employment and one has part-time). If people want individual bank accounts so they don't have to explain every purchase, or just so they don't inadvertently overdraw with simultaneous purchases, I think that's fine. My husband and I have separate accounts to manage, but we just move the money back and forth as needed depending on who had a bigger month financially or which one is elected to cover a big expense like putting on a new roof. A friend of mine has a child with her first husband, so she and her second husband have 3 accounts - the household account for all the big stuff (mortgage, utilities, etc.), his account (for his personal expenses and activities like game tickets and golf) and her personal account for personal stuff as well as the child's stuff (child support goes in, child's dental bills and activity fees go out without there being any question that any of it goes to the second husband's expenses).
My husband and I started out with separate accounts when we got married, and he had children from a prior marriage, so it made sense to keep things separate in the beginning. We just kept it going because it continued to work for other reasons. For example, if I order something for his birthday, I don't want him to see the charge for it on a credit card statement or in the checkbook register. He likes the same freedom. It's not about insisting on anything - it just works.
My husband and I don't divide along "traditional" roles so maybe that makes it easier. Maybe we just communicate better. I don't know. But it works for us. We don't assume that our division works for other people. So you should do what you want and what works for you. But you are clearly in a marriage based on respect - and as we see on this site, not everyone is in that place. Moreover, not every woman was raised to value what she does in the home, and not every woman has your strong sense of herself. So if she needs a separate account, or wants one, to help her on her journey, I see no problem with it.