Re: “if the players aren’t going to, or can’t, engage with or don’t know about the Big Things, why bother having them? … The outside events have to matter and they have to be transmitted somehow, but they can’t narrowly constrain the sandbox otherwise it’s not a sandbox any more, right? ”

My (early and poorly organized) thoughts on this: The purpose of having the Big Things going on in the background is to partially alter the nature of the sandbox.

Not too tightly, as you point out, but somewhat. This changes the nature of the playing field, and allows for a feeling that the world is dynamic and changes. Partly due to the PC’s actions, but partly because it is ‘alive’ (or at least, that’s the illusion we give.)

Strangely (or perhaps not so strangely) the example that comes to mind is from Lord of the Rings Online MMO. Human characters begin the game in this village, where you do the usual tasks and is kind of sandboxy… until an Event comes to pass, and (spoilers, I guess) the village is attacked and goes up in flames. Now the PC’s intervene in the battle, and some fun things happen, but the aftermath is that the village is burnt. You can’t go back and play in the area anymore. At least not under the same circumstances.

I think this is fun in the tabletop RPG sandbox setting too. Your players have made the Village of Home-let their home base? After a while, maybe it’s fun if it burns down. Now they’re no longer settled in, and have to move and perhaps encounter a new village or city to use as a home base. Keeps things fresh and interesting and moving along…