We can, but since the game doesn't show the results, why would we? If the game continued after the slides, and did show, that would be interesting, but I doubt that ever happening. I'm not totally against playing after the slides, but people generally want to see the result of their actions, and that just isn't happening. So it's either restart a new game, or have a mindless non-canon bit.
You can continue exploring the world before the slides too. There's nothing saying you can't. But if what you want is that after the slides, the game to continue and expect to see the results of what you did in the main story, and side stuff, that isn't going to happen. And it's for the better that that happens, because as I said, the PC's actions had consequences that take months or years to come about, not something that happens overnight.