Hair of the Buddha

How much is known to support, to refute, or to expand upon the following viewpoint? *The Buddha shaved his head like all his bhikkhus.* Supposed reasons to backup this viewpoint are: - There are references in the Pali Canon where someone calls Gotama a shaven-headed recluse. - There are other references, like in the Ariyapariyesana Sutta (MN 26), where The Buddha explains that he shaved his head when he went forth. - Buddhism arose during an an-iconic period, so depictions of the Buddha were frowned upon. - Artistic depictions of the Buddha are relics of the Ghandara Buddha-statues, created long after the Buddha's death. - This representation was spread to other Buddhist regions over time. Quite curious what can be said about this topic.