I'd argue that both scales do indeed "start" and "end" on the same note - middle C. If I were playing an arpeggio that spanned both staves, I think I'd find your method harder than simply moving in thirds from the E on the treble clef to middle C to the A on the bass clef.

Interestingly enough, other clefs do already exist. The "C" clefs (alto and tenor clef) identify middle C and simplify note reading for instruments that have atypical tessiturae.