Why is 3. Nc3 so rarely played?
Because Black can play 3...e5, which transposes back to the 3.e3 e5 line after 4.e3 (4.d5 and 4.dxe5 are nothing), but 3...a6!? is really challenging for white: 4.a4 is not a move he would like to play.
On your suggeted 3.Nc3 a6 4.e4 b5 5.a4 line, the move 5...c6 transposes directly to the aforementioned Adhiban- Nakamura game (Poucin's #11), which Naka has published with extensive comments, and claims that Black is doing fine.
Well that is why I was inquiring. I enjoy chess but clearly not as advanced as others (and yourself) and I was inquiring why 3. Nc3 was so underused as it's something I've inherently played over the years in QGA, right or wrongly (as is more likely the case). Was just a question.
I have played 4. e4?! before but I find ignoring the QS push is the best way to maintain parity. 4. e3 does offer a bit more solidarity for lack of dynamic play.