Action games may be the minority of all games
developed, maybe. They're definitely the most desired and most market viable. It's easier to write a turn based game in garbage collected language. There's a surplus of these games, so they don't even sell well.
The best selling console games are sports simulators and first person shooters. The next popular are open world RPG/action (Skyrim, Fallout), then we have fighting and racing games. 2.5D platformsrs are also popular now. All of these games need the deterministic guarantees of "fast twitched action games".
It's not so much performance as much as control. Objective-C is a lot slower than C++, but making action games in pure Objective-C is viable because you are still in control of a system that allows for deterministic resource cleanup and stable frame rate.
In the US, I'd say turn based RPGs and puzzle games are by far the least popular genre on consoles across the board. They may be most widely produced games, they are hardly the most widely consumed (
outside of Mobile).