Considering more games are having it then I expect it will keep increasing.

I dont think it matters enough to "Play a huge part" of the next gen.

I think Minecraft, Fortnite, Power Rangers, Mortal Kombat, and Call of Duty have brought the walls down on cross-play. I'd expect to see it much more often next generation. There's no excuse now.

which games would you like to see cross-platform play?

Every competitive game I own.

I imagine third parties want it.

Fair enough cowboy. :)

Another important aspect is competitiveness. If console players weren't able to play against PC players, they'd never improve to a level where they could compete with them. That's why there are actually good console players in RL. I sometimes even see one or two when I queue at GC level.

It's big, but idk about huge. The games that really benefit from cross play aren't the "huge" games, so most people won't really care. You can play games like Fornite or Calls of Doodies with other platforms but it's not needed, none of the platforms suffer from any lack of player base. But some of my most played games this gen, like Evolve or Battleborn, I own on PS4 and Xbox, and Evolve is already dead with servers offline. It had a low userbase problem across all three platforms. Every user would have greatly benefited from cross play. Battleborn servers are going offline in early 2021, and on all three platforms it's almost impossible to find public queue matches, you have to manually setup matches because of lower userbases. Cross play would benefit everyone here. I would imagine there will be plenty of games next gen that fall into this same category.

It's the future. Sony will be reluctant and greedy, as they have been. Xbox, Windows, and Nintendo will embrace it more than ever.