c4 and d4 both have better odds at master level.
Is 1) Nf3, The Strongest 1st Move?

Wouldn't opening up lines for bishop and queen whilst controlling some centre squares be better? Like good old e4?

Nope. You would be advised not to bring out the Queen through there at all.
While the Bishop if moved with
Pointless aims at f6 from Black.
Which is why GrandMasters rarely play Bishop's or Guocio Piano.
But the Spanish/Ruy Lopez still remains promising. But entails 2) Nf3 First.

Nf3 is best according to the computer because it waits for black to show his cards before white. But from a human perspective, e4 and d4 are the best as they directly control and occupy the centre.

A lot of stuff that starts with 1.Nf3 ends up transposing into d4 and c4 openings. In fact, if your opponent plays 1...c5 you can even transpose to a Sicilian.
Yes and 1) Nc3, cover the most squares on move one.
But Nc3 can be attacked more easily with; 1)...d5 2)...d4