Yet I have flown over 500 flights, many of which (half?) booked through OTA's, and never had a problem that couldnt be resolved. That doesnt mean problems never happen (and your example is pretty much the worst one - a few days before departure), but for me, it has worked out well. All rebooking issues have been taken care of by the OTAs and in case of IRROPS you always go to the operating airline anyway.
But I do have a tactic. I don't book through an OTA if I expect that the flight may need to be changed. Also I don't use OTA's if I want to be sure that I'm able to upgrade. And, I always use them only for European flights where, in case there were to be a problem, I would be able to find an alternative fairly easily. And in practice that means that a few times I have had to throw away unused flights because the change fees through the OTA would be higher than their value. Thats part of the game.
So I guess I would agree with your insurance analogy. Generally I don't go for insurance either
After all, insurance companies only exist because the chance of not needing them is higher than the chance of needing them. As long as you are aware of your choices and the possible implications, you should be fine. But, as with everything in life..do your research first.