Is there space for (another) notes product that is purely focused on the GTD framework? Would people use this if I created it?
In my experience, there are plenty of excellent software tools, on the surface. If you want to innovate, I think you might want to think broader -- about how GTD systems actually succeed or fail.
If you were to ask me about the weakest links in GTD software, it has less to do with the "core" software and more to do with behavior. Challenges I've seen include: (a) Forming the habit to use a new GTD tool; (b) Continuing to use it even when life gets in the way and you revert to another system (such as using email, ug); (c) Making it appealing to return to after a break, knowing that there will left-over cruft in there.
Many successful entrepreneurs started by inventing a new to-do list. This is because it is the only way to come to terms with what it means to get things done at all.
There is literally no better use of a first-time entrepreneur's time than reinventing to-dos.
If for no other other reason than due to the sheer absurdity of the idea of procrastinating over creating a to-do list. It's something you can't help but do immediately, and is "self-hosting"!
I might have been exaggerating, but I think it's a good exercise in coming to terms with your abilities and task management ideas in general, to create your own to-do system ahead of anything else you're doing.