Related to this is the recognition that, to date, every trek show (though TOS was more ambiguous) had men do the cooking.
Well, that's an old stereotype... Men are chefs (they go out to work to cook & get paid for it), women are cooks (they stay home & feed the family).
It's so pervasive, though, that I know female pastry chefs who had a hard time getting used to being called "chef." They called themselves "bakers." And these are pastry chefs who are recognized as among the best in the world.
You're right on the stereotypes and that some pastry chefs prefer
being called "baker." I think that "bakers" are actually more specialized chefs, so they should want the recognition of achievement in their specialized field. On the various tv cooking shows, many of the chefs, for all their ability, are damn afraid to bake, while the bakers are willing and able to cook at the same high level as the chefs.
Go bakers!
Baking is much more precise & a good pastry chef/baker understand the chemistry involved.
Many on the savory side are baffled by that part.
Me, I love the geekiness of the science behind baking & jam making & the like. :-)