People wanted more direct control over the GPU and memory, instead of having the drivers do that hard work.

To fix this AMD developed Mantle in 2013. This inspired others: Apple released Metal in 2014, Microsoft released DX12 in 2015, and Khronos released Vulkan in 2016 based on Mantle. They're all kind of similar (some APIs better than others IMO).

OpenGL did get some extensions to improve it too but in the end all the big engines just use the other 3.

OpenGL cannot achieve the control over modern hardware necessary to get competitive performance. Even in terms of CPU overhead it’s very limiting.

Direct3D (and Mantle) had been offering lower level access for years, Vulkan was absolutely necessary.

It’s like assembly. Most of us don’t have to bother.