By socially constructed time units you mean how many times the earth has gone around the sun??
I wouldn't call it arbitrary (a year). It is a hard number and affects almost every aspect of our lives such as food production, travel, navigation....etc. Age is also important when it comes to determining overall health among other things.And why would we care about such things? It's an arbitrary measure and humans apply the meaning to it, like that number matters. We build the meaning and weave it into our culture.