Why is s'abonner reflexive?

Your reasoning is exact in what concerns « se régaler », as it means “to enjoy oneself doing something” (the English seems to confirm the principle here!); there is no action performed on the subject, which makes things rather annoying; again, this verb means “Au fig. Éprouver une vive satisfaction d’ordre esthétique ou intellectuel.” (TLFi); this is the description of a state of mind, not an action; if there is an action it is that of food on your palate, or of pictures on your mind when watching a film; you are then just the recipient of an action; therefore we are in the domain of the idiomatism and not anymore that of functional construction of forms; it is an exception to the principle.

The second instance is not correct; it does involve an action, but the object of the action really is the person doing it; the construction is “s’abonner à” (Je m’abonne à la chaîne X.); “chaîne” is a COI, not a COD.

“S’abonner” means “to impose to yourself certain ties according to the rules of a given organism in such a way as to be the beneficiary of given advantages from that organism”. You are, then, performing an action on the “administrative” part of your life, at large, yourself; that’s the way to conceive this action upon yourself (the subject).

Complément à l’autre excellente réponse.

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