Here is a game I recently played on chess.com that shows the importance of quick rook development. I definitely developed my rooks before my opponent developed his which ultimately won me the game. You will notice how I develop my rooks quite early and the queen as well. Always be careful when developing the queen early. This time it worked out quite well for my queen. I almost seem to tease my opponent in helping me develop all my pieces. With you pieces developed on good squares early it can open up a lot of opportunities especially if your opponents development is a little behind. I was also able to keep my opponent from castling and that in itself is also a small victory as well.
My opponent resigned here. To complete development, imagine moving the knight on a3 with tempo attacking the queen on your next move. Finally all that remains is to somehow try to open up the f file for your other rook. Alternatively you can also move it on the D file. The only treat my opponent had is a check on move 14 which was a little trap that ultimately helped me develop even further. You could even say I got pretty good compensation for not taking that bishop 1 move earlier. My opponent did gain a pawn but was a good exchange for developing a bishop and putting a rook on the 7th rank. Finally I hope that you have enjoyed my game on quick rook development.