I remember hearing I think it was a Radiolab episode which talked of an instance where a lot pollination was done by humans, by hand, with paint brushes and pollen. It turned out that the humans were actually better at it than the insects, because they were more consistent. So the result was a crop that was larger than it would have been had insects done the pollinating.

It's kind of a "waste" of human effort to do manual pollination like that rather than having insects do it "for free", but in an emergency, if that's all you've got, then it can be done.

It also seems to me like this kind of work would be ripe for automation with robots or drones somewhere down the line if, say, most bees wound up dying out and humans were forced to pollinate by hand at a large scale.

It isn't so bad. Pollinating hundreds or thousands of flowers by hand in an hour is imaginable.

Better to have friendly insects do it, but if you want the fruits, having humans step in is viable (it is or at least has been done for apples in China).

There's also a lot of plants that self or wind pollinate (most grains).

The vault against the story the media try to tell is not for mankind coming back from some apocalyptic event. It works like a bank vault. Anyone who wants can pay them money to keep sets safe. The common use case is for protecting seeds of crops your country cares about in case some pest kills all the crops or similar. Not for Mad Max.

Using drones to perform pollination would not be too difficult I wouldn't think...