Raidou is bald.He's a man with spiritual training. Depending on the extent of the Buddhist influences on the Kuzunoha clan's traditions, he may be required to keep a tonsure. But he's vain, so he only does the top and wears a hat to cover it at all times.
Raidou's hat is the true source of his power.That's why he can never take it off. Narumi's hat is the source of his detective abilities, too. In fact, the entire game runs on the power of Nice Hats.
The Shin Megami Tensei main series (and Imagine) and the Persona series (and possibly Shin Megami Tensei If) are both possible/alternate futures of the world of DSRKClearly the canonical future is that of the Shin Megami Tensei main series, since that's the one we see in the Akarana Corridor and the one the crazy Messian Raidou possessing Kaya came from. However, Persona 2 also features Kuzunoha summoners, who seem to be running a detective agency — which would make sense if Raidou got a taste for detective work during his time with Narumi and decided to set up his own business later on. It could just be meant as a Mythology Gag / shout-out to the earlier two Devil Summoner games, but there's no real reason why it couldn't be the future of DSRK... except that the main series timeline and the Persona series timeline are completely incompatible. But we know that alternate universes exist, and that history doesn't always take the same course in each of them, so...