It makes me think of a big budget game made by a company that makes big budget games and primarily publishes them through mainstream channels. It makes me think "opposite of Indie". I don't think that there's an indisputable, unambiguous definition of either term.
Yes, when they have a choice and resources. It's not even the case here. I.e. it's not like developers simply prefer lock-in when dealing with some of the walled garden platforms. They simply have no choice - the likes of MS, Sony and others don't leave them that choice. It's not a discussion on technical merits. You could use your logic if developers could actually choose.
And if you don't have resources to ask/communicate than just use something like https://github.com/bkaradzic/bgfx/ which is an awesome API agnostic rendering library.
What would be the point for them to use the benefit of cross platform API, if they need to write their own? It won't be any cheaper than using the existing lock-in.
What's big and bulky - shaders themselves, but there are solutions to translate them between different available languages.
Those solutions aren't really ready yet: https://github.com/KhronosGroup/glslang/issues/200
> No, indies will demand it.
> AAA studios are doing quite fine with the current API that are even lower than Vulkan.
Meaning of "AAA" is totally mixed up, so there is no point to use this term without explaining what you mean. Indie might mean independent indeed, but what AAA stands for is completely ambiguous. You might mean projects with big budgets, but they can be independent as well (Star Citizen), so you can't use it as some universal category. For the reference Star Citizen is going to use Vulkan.
Regardless of what "AAA" is supposed to mean, they will use whatever will cut their costs to do the job well enough. And cross platform options surely will, if they'll be available.