I did all of mine individually.
I also did it a few years ago, and there were significantly less games, or you've got all the clones in there too.
The reason for this is that not all games work properly for player 2. Sometimes the screen flips but the characters don't, or the buttons are screwy or whatever. (I reported the bugs that I did find)
It's a PITA for sure, but hey, you're play-testing games. It's not like you're painting the house or similar. Grab a beer and make an evening of it. You will also get to know your machine better, you'll be able to visually inspect each game for resolution or volume issues too.