but isn't it also likely that a distant ancestor was, in fact, a baker?

Could be. Probably was. But all the non-baker Bakers in the world surely outnumber the baking Bakers. Also, the word baker (< OE bæcere) predates anybody with that name, I would suppose. And, all those non-Bakers are referred to as Baker because that's the name they inherited from their father (or chose for themselves, or married into a Baker family). I was talking about the origins of words or the semantics of words.

or have I completely misunderstood your point (once again)?

Well, I guess I didn't state it well. I tend towards the nomos (convention) side of the scales when it comes to semantics. I don't think there's much in b and k with a vowel in between that signifies a person who bakes or the process of baking.

Ceci n'est pas un seing.