Just a quick comment on space being utterly predictable, that is not the same as being predicted. In the area in which spaceships will be operating, there are a variety of forces working on objects - mostly gravity but also smaller forces like solar wind. Objects will eventually reach stability or crash into something, but this can take millenia on the scale we are talking about.
What might a spaceship crash into? Biggest worry would probably be debris,say from a space war a few centuries ago or from a mining operation. Then again, at a relative speed of 100,000KPH, a candy bar wrapper (which could have been in a airlock when it evacuated) would pack a considerable wallop. I'm sure just about all naturally occurring 'junk' would not be a problem unless something really nasty happened recently (in solar terms) , but 'junk' leftover from 1000 years ago can easily still be around to cause problems.
Space may be vast, but the area where ships travel isn't as big, already Earth orbit has a litter problem and we have barely even begun to enter space. Sensors can be powerful and detect small objects at long distances, but if that object is moving at .01c (relative) the sensors have to spot it at 1,000,000 meters just to have a fraction of a second to change course, which might be a problem for the sensors if it is something small as a screwdriver.
Not that I'm saying it is inevitable that space travel will be dangerous, but that it is not necessarily utterly safe.