Primogeniture

Query: is primogeniture constitutional? If a state were to require that all property passed on at death go to the eldest child (with no requirement of maleness or legitimacy) would such a rule pass constitutional scrutiny?

Somewhat weirdly, I think the answer is yes. Birth order isn't a suspect or quasi-suspect category, and as such the measure would only have to satisfy the rational basis test. And surely one can devise some rational basis for such a rule. (Say: it prevents the fracturing of estates that might produce anti-commons problems.)

And yet: that can't be right. Surely I've missed something. Thoughts?