One problem I see with that is ledger lines. They are hard enough to read as it is. With your 6-line system, it would get out of control. Unless you have added some additional complexity to read an octave up or down.
There’s been different approaches advocated for that. For extended above the staff passages, the standard 8va and 16va notation could be used. For short segments, or a note or two, there have been various proposals such as a triangular shaped note instead of the usual dot shape indicate it’s played up an octave from what‘s notated. But those are are topics for a different thread since the discussions and examples would take a thread all by itself. Suffice to say the discussions about alternative music notation systems that more closely match what we’re currently composing is ongoing.

I like to tell guitar players, "Pretend I'm a piano player, and tell me what key you want to play it in." They usually still have no idea.