On the other hand, I find the attitude that crashing is an inevitable part of cycling very trying
Ah crap. I had a car crash into me today.

I was at a staggered crossroads and going straight across the stagger into a no-entry-except-cycles road when a motorist coming the other way didn't keep left and turned right across me. Looking at the video now, it looks like they didn't indicate, but my handlebar camera only saw them for about 2 seconds - how fast do Skoda indicators flash?
Anyway, I emergency-turned left (towards a rather solid brick wall!

) but their right wing mirror still caught my right handlebar, disconnecting my gear cable (and snapping my click box as a result, which I didn't notice until I tried to ride on). No contact with me. I put a scratch about 10mm long on their wing mirror. So about £50 of vehicle damage each, I reckon. We shook hands on it and agreed not to take it further. Now I wonder whether they settled because they shouldn't have been driving on that resident-access-only road... but never mind. I've saved the video just in case.
Really, the most annoying things were riding home stuck in 46" gear (27" x 48:28) and the Dutchie being out of use for 2-5 days until replacement parts arrive (if it was a Sturmey 3-speed, two local shops stock spares - another reason to change).
I came back here because I thought I'd have to update my answer but I didn't come off this time so it doesn't change my answer to "Have you ever come off your bike?"