Universal default is the term for a practice in the financial services industry for a Lender 1 to change the terms of a loan from the normal terms to the default terms (i.e., the terms and rates given to those who have missed payments on a loan) when Lender 1 is informed that their borrower defaulted with Lender 2 or 3 or 4, even though the borrower has not defaulted with the Lender 1.
Universal default was once common for credit card debt. Universal default for credit card debt was banned under the Credit CARD Act of 2009. If you were defaulting on credit card at Lender 2, and were current on a credit card payments at Lender 1, then Lender 1 would not be able to default under the new law. However, if both of credit cards were issued by the same bank I see nothing in the Credit CARD Act that would prevent the bank from closing both accounts if you default on one.
You are asking about universal default that is truly universal and not just among the banks issuing credit cards. I am unaware of any such truly universal default across all tradelines. There is a type of universal default called "right of offset" that allows a bank or credit union to remove funds from (for example) a customer's checking account if he or she fails to make payments on a car loan from that same bank or credit union. That is why some financial experts recommend consumers with a mortgage from a particular servicer not bank with that servicer in the event that if the consumer falls behind on their mortgage payment they do not discover an empty checking account drained by the mortgage department at their bank.
In a perfect world, it would be wise to contact other creditors to reassure them you had no intention of defaulting on your payments if you default on another account. However, the world is not perfect because people and systems are imperfect. The risk to contacting your other creditors with this information is creating misunderstanding. A harried customer service representative may misinterpret your statement, whether it be on the telephone or in a written letter, and may check a box in your file stating that you are about to default on your account.
You assume that all creditors will receive notice of your default through other means. They may not. Some creditors, such as mortgage servicers, seem to watch customer credit reports for signs that the customer is about to refinance, and it is likely a mortgage servicer would notice a default on another mortgage. Other creditors pay no attention to customer credit reports. The ignorant will remain blissfully unaware you are defaulting on a mortgage as long as your account with them is current.
Should a creditor contact you following your mortgage default and ask if you intend to remain current on your account with them, by all means state what you did in your question above. However, I believe the cliche "Let sleeping dogs lie," applies to your situation.