For other demons, you simply wouldn't get near enough for that kind of affection. Demons don't trust each other, and it's very wise that they don't, so they keep a certain level of distance between them at all times.

In Aziraphale's case, it was because touching him was akin to putting your hand on a low voltage wire. Not painful, but with a noticeable tingle.

When it comes to Elizabeth... it's because she's human. He doesn't expect her to understand that, but he doesn't stiffen up against the contact like he did the first time. Instead, he sighs and pats the back of her head lightly, then wraps his arm around her shoulders.

"I really hope you never have to witness how truly cruel the world can be."