IMO, this is a common misconception. Or, at least, the extrapolation of it is. Vulkan might require a lot of code to initialize, and has extra responsibilities related to memory management, synchronization, etc., but in my experience the end product doesn't require significantly more code than other graphics APIs. The up-front cost you pay doesn't translate to increased costs everywhere else, at least not to the same degree.
My library supports D3D11, Metal, Vulkan, and OpenGL, and Vulkan is the second-largest backend, but not by a lot (LOC: ~5k Vulkan, ~3.3k D3D11, ~2.5k Metal, 6k OpenGL). LOC is not the best indicator of complexity, to be fair. My OpenGL backend is definitely the most difficult to maintain and the largest, because the API is such a pain to deal with.