Yes, you can get very close to that API with this extension + existing Vulkan extensions. The main difference is that you still kind of need opaque buffer and texture objects instead of raw pointers, but you can get GPU pointers for them and still work with those. In theory I think you could do the malloc API design there but it's fairly unintuitive in Vulkan and you'd still need VkBuffers internally even if you didn't expose them in a wrapper layer. I've got a (not yet ready for public) wrapper on Vulkan that mostly matches this blog post, and so far it's been a really lovely way to do graphics programming.

The main thing that's not possible at all on top of Vulkan is his signals API, which I would enjoy seeing - it could be done if timeline semaphores could be waited on/signalled inside a command buffer, rather than just on submission boundaries. Not sure how feasible that is with existing hardware though.