No, it doesn't have anything to do with its etymology, although it's an interesting one. It's just that haber is an impersonal verb per se. Follow the previous link and look for the meanings marked as "impers.". You need to use se when using a non-impersonal verb (such as deber) in an impersonal sentence.
The meanings of haber in such sentences are these ones:
- impers. Estar realmente en alguna parte. Haber veinte personas en una reunión. Haber poco dinero en la caja.
- impers. Hallarse o existir real o figuradamente. Hay hombres sin caridad. Hay razones en apoyo de tu dictamen.
There are many impersonal verbs, most of them being related to the weather: llover, nevar, granizar, atardecer, diluviar, brisar, and so on. None of them need the se to form sentences.
Note that you still need to use se with haber when the verb is not used in any of its impersonal meanings:
Se ha de venir bien vestido.
In the case of the last example, the meaning is not impersonal:
- aux. U. con infinitivo que denota deber, conveniencia o necesidad de realizar lo expresado por dicho infinitivo. He DE salir temprano. Habré DE conformarme.