Yes, except it doesn't seem to be working.
> It protects a dependent spouse (say, a mother who chooses to stay home and care for her children instead of producing her own income) from abandonment by supplying the dependent with legal recourse for support even if the breadwinner decides to blow it
In theory yes...in point of fact, it doesn't always work out that way.
I could pick apart your extremely loose reasoning more, but let's get down to brass tacks. Your entire argument is predicated on the notion that "family" === Mother, Father, and biological children. This is patently absurd.
There are millions of infertile, adoptive, heterosexual couples who by your implicit argument don't deserve the protections and rights of marriage. However, if you expand the definition to include them, you must include homosexual couples too.
You're partially right. Marriage encourages stability. I would disagree that is the only reason for it though. More importantly what you're missing is that it's beneficial to society to have ALL families stable...regardless of whether they have biological children or not. It makes for a healthier and happier population.