It is possible to derive this information but it's real pain the backside to do so.
I use the Experian Credit Expert site to periodically check up my credit rating information. One of the sections is financial associations and it lists everyone your record is linked to. If the rest of your information is fine then you can see who might be causing you problems. However all you have is a name and you have to get that person to obtain their own credit report.
I certainly don't see any reason why two people who want to establish a financial relationship shouldn't at least be able to get an idea about the other persons financial state before they sign on the dotted line. In the case of marriage/civil partnership then that should be automatic.
Surely that would actually put people into more debt to start with. If you are only permitted to pay the minimum payment for a few months you'll be racking up debt.
It would surely make more sense to start with a low credit limit and see how much the person pays off each month as it rises. People who only pay off the minimum amount each month would be seen as a higher risk than those who pay off larger amounts (or the full amount) each month and the credit limit could then rise progressively to whatever maximum is agreed between the customer and the bank. The rate at which the limit rises would be set depending on the repayment rate (minimum payments get the slowest or zero monthly rise while those who pay off the full amount each month get the fastest monthly rise, say after a delay of a couple of months).
The problem with the above system is that it seriously penalises people who do manage their finances properly as they get treated as if they don't. It's would also effectively kill off the usefulness of 0% balance transfers and purchase deals for those who do use them responsibly (mind you I doubt the banks would be heart broken by that as they make very little money out of these people).