I often see "deshou" instead of "darou" in text where only plain, casual verbs are being used, that is, a converstation between friends, for example. Why is that? Why not darou?
In casual conversation (i.e. even when only plain, casual verbs are being used), women/girls (and young children too) tend to use 「でしょ」「でしょう」「でしょー」 etc. instead of 「だろう」「だろ」 at the end of sentences. 「だろ(う)。」 sounds more masculine and 「でしょ(う)。」 sounds more feminine and softer in casual conversation.
でしょう and だろう will often be used by same people in the same conversation.
Even males tend to prefer でしょう over だろう in most situations unless they're really going for that masculine feel or talking very casually.
でしょう since it is polite will often be used to get approval or talk about another person.
でしょでしょ？ Right right? あるんでしょ There would be/ they would have it etc
In these situations using だろう could seem a little harsh or stand-offish
On the other hand when wondering to oneself since you're not talking about other thing だろう is more natural in casual speech.
なんでだろう？ why could it be？
I checked the hits on google and あるんでしょ has about 4 million more hits than あるんだろう whilst なんでだろう has 4 million more than なんででしょ so it really does depend on the type of phrase more than the level of politeness.
In practice, within a conversation, the final verb form may be used to help convey an inter-personal meaning attached to a particular sentence. Using "deshou" instead of "darou" in a sentence temporarily assign the listener/reader more respect to emphasize the doubt on the part of the speaker/writer. Assuming this is the reason, then it is not surprising that it occurs with darou/deysou, because indicating doubt is often a deliberate indicator of humility.