What is the consequence of removing the two-square first move rule? In this related question I see that en passant and two-square first move for pawns were introduced together between 1200 and 1600. What was the reason for adding these rules? Put another way, has the variant of chess without the two-square first move rule been studied and found to be less interesting or enjoyable?
The purpose of the two space first move rule was to speed up the game, and the (military) theory behind it was that soldiers leaving "camp" and marching to the "battlefield" could march at double "time" (speed) before the actual fighting began.

The one thing that could prevent this was an enemy pawn on his fifth rank (your fourth) adjacent to the marching pawn (soldier). Think of your soldier as being "ambushed" by the enemy en passant on the way to taking up his designated position on the battlefield. He never arrives there, even though his marching orders tell him to march two squares in one move.

Not having these rules would make for a slower game.