The latter is definitely not the problem. Even the Twitter re-design from a couple years back still supports all the old hotkeys.
All it takes to at least support a tab-based workflow is using the "tabindex" property if your form isn't logically laid out already, and the rest can be done by capturing hotkeys.
Even multimedia content can be operated using hotkeys. Youtube is a good example. There's no excuse but laziness and incompetence IMO.
[1] https://developer.mozilla.org/en-US/docs/Web/HTML/Global_att...