Again-The mortgage is a legal construct for a secured loan. The collateral is the property. The lender has a legal lein to that collateral should you not meet the terms of the contract. When you write a mortgage contract, there has to be a legal connection defining ownership back to the mortgagor. If you were not on the deed, there is no such connection. The lender cannot attach a lien to the property since you are not a legal owner, thus making it an unsecured loan. If you walk away, they are left holding the bag. They would never approve of such a scenario.
The deed is a legal construct that provides proof of ownership. The number of owners is irrelevant. In your case, you are joint tenants of the collateral, the property, even though your wife is not listed as such on the deed. Her claim to ownership is that she is your lawfully wedded wife. The lender still has the primary right to foreclose should YOU, the mortgagor, not meet the terms of the obligation. Your wife is second in line.
If you are not married and you add someone to the deed as a co-owner, it is your prerogative. Nothing I would recommend. From the lender's perspective, it doesn't matter. They have the primary lien should something run afoul. They always come first. The other owners stand in line.
An excellent explanation. Appreciate you filling in the blanks with that one.
-LD