My assumption for allowing only elites to standby for a later flight, was that standing-by-for-later, is in some sense, a no-show. Yes, flat tire rule exists, but this formalizes the courtesy for elites. And sure, an elite could be physically present at the gate for their ticketed flight and still have prior intent to standby for a later flight (therefore not exactly no-showing in its purest sense), but that seems rare.

That said, your explanation also makes sense, and I will now have an additional explanation in my head.