I've only flown EK on one trip SFO-DXB-BLR, but on 3 of the 4 segments the flights looked fairly empty up through OLCI, but ended up almost fully packed (the 4th, the initial SFO-DXB leg, showed full earlier and was). I don't know if a large number of people can't or don't bother making advance seat selections (I had issues with doing it online and had to call) and get assigned at the airport, but it was a lot.

The risk in doing the above is that you'll get to keep that middle seat and end up with 3 people around you. It's certainly worth trying for an empty seat/row by choosing an aisle in one of those rear rows, but don't be surprised if it ends up full.

One hint -- choose a right-side-of-the-middle aisle seat; I had a left aisle seat and the seat next to me got filled, but the other middle was empty (one of the few seats on the plane); I assume the automated or manual choice subconsciously picked the lower letter first.