It’s partly because of conservatism in traditional grammatical analyses of French, that made a strong distinction between personal and demonstrative pronouns and have roots in the grammatical system of the 16th and 17th centuries, a time when cela was only beginning to reduce to ça and hadn’t really gained its modern functions as a personal pronoun. Demonstrative pronouns are a common source of personal pronouns after all, and indeed that’s how il(s) and elle(s) began their career too.

(I’m mentioning ça because ce function at its allomorph when used with the verb être, they’re functionally two forms of a single morpheme)

In practice, ce/ça is the clitic (weak) subject personal pronoun used for non-specific or non-Noun Phrase referents:

• La course, elle me plaît (“I’m enjoying this race”, NP specific subject so il/elle is used)

• La course, ça me plaît (“I enjoy running”, NP subject, but since it’s generic ce/ça is used)

• Courir, ça me plaît (“I enjoy running” non-NP¨subject, so ce/ça is used)

You could extend the same analysis to ça in its usage as a strong object pronoun (“Les pâtes, je les aime” vs. “les pâtes, j’aime ça” vs. “manger des pâtes, j’aime ça”).

Ce + être is also the copula, which is what’s happening in the question’s sentence “Robert, c’est un médecin”. In this case, it would be abusive to call ce a pronoun at all: it has no real referent and only functions as a bleached grammatical marker.

While traditional grammars and most pedagogical material don’t classify ce/ça among the personal pronouns, you can find some that do, especially those written by linguists. For example, the always very complete “grammaire du français langue étrangère pour étudiants finnophones” does, as well as Paul Rowlett’s generativist “The Syntax of French”, for a non-exhaustive list.

For further reading, the author of that first grammar has a very comprehensive article arguing for large scale review of the 3rd person pronouns and their extension to some forms usually classified as demonstrative: KALMBACH Jean-Michel, “Le système composite du pronom de 3e personne en français” in Langue française 2014/1 (n° 181), p. 97-117.