I understand what is being proposed. Nonetheless it would be better if the word “marriage” was recognized. If two people enter into their own marital contract, and that contract is regarded as valid by the government, then by definition the government has just recognized a marriage. If alternatively you are proposing that no couple be allowed to enter into a marriage contract (they would simply have to call it a contract), then that would be a horrific interference in peoples’ personal lives. It would mean that couples couldn’t enter into private contracts of their own design.
Finally, even if this system were workable it would not be desirable. The word “marriage” carries with it a social value that “business partner” and equivalent terms can’t match. It means that two people have entered into more than a passing commitment. Most people regard it as much more serious than signing a lease to an apartment or buying a car or merging two companies. Linguistically this should be accounted for, and I can’t think of any word other than “marriage” that comes close. Asking all of society to give it up or rename it to something closer to a business relationship would mean that as a social institution marriage really would be devalued.