Delays on your commerical flights would be covered,
Actually when I called my agent about my situation, their initial reaction was "when the airlines have a delay which necessitated an extra night in a hotel, then the airline will have to pay for that, so we don't". And that was before these new EU regulations came into place that requires the airline to pay in a lot of situations when there's a significant delay.
So I think the travel insurance will only pay for an extra night in a hotel when there are exceptional circumstances that would release the airline from the liability for that.
With regards to renters insurance, I always assumed that the school from where I rent, would have this priced into the price of rental?
Me too.
But now that I'm thinking about it - you might also want to check your (domestic) life insurance if you have any. (And there might be one attached to your mortgage.) Some of these specifically exclude private flying, or place significant limits on them.