You are refereing to cohabitation agreements which already exist. You can just educate people to enter into those "mere contracts" rather than getting married.
As an institution rather than just a contract Marriage is afforded certain priorities that are not available in mere contracts.
For example, despite what a will has, many states have mandatory widow's/widower's shares.
For example, child supoprt would be fixed under a mere contract concept rather than as the cost of living adjusted system now.
Those the want only contracts have been free to do so for decades. cohabitation contracts are readily available from various form companies.
However as a institution marriage as a means of producing and raising children is paramount to the continuation of a society. This is not to be left to the haphazard contracts any more than one would want to privatize the US navy to france.
If the government no longer defines marriage, then does it not follow that mandatory widow/widower laws and the like will be void and thus able to be replaced by contract?