I think this would be one of the reasons I would want an NGPC. The one person I knew with NGPC only liked one particular genre (I'll let you guess which one) and... this seriously limited my enjoyment of the handheld.
I'm going to guess fighters. Was it fighting games?
...all these years later, and I'm still a bit disappointed in all of the NGPC fighting games. I wish the system had included 4 buttons but beyond that, I think the system really should've included layered sprites. With only 3 colors per palette, you just couldn't make the characters look good. Black, white, accent color.