What I understood is that if you've deleted a lot of e.g. objects in one go, your game is more prone to crashing if you haven't cleared your Thumbnails cache.

But what about the likelihood of crashing if you just have cleared your Thumbnails cache files and your game crashes when loading a random Buy/Build Mode catalogue? (assuming there are no obvious broken Objects around)

I don't think thumnails cache size would cause crashing, but if you commonly add and remove a lot of custom content then the file size of those caches can get larger than needed, as there will be a lot of thumbnails in there for items you have removed.
If you delete the whole folder then the game will copy over a fresh set, with just the caches for the Maxis objects in there. When you next access CAS or the build/buy catalogs, the game will lag as the thumbs for all of your CC have to be built again, but should run as normal once you've accessed these items once. You have to give the game time to rebuild these caches so scroll the catalog slowly. Smaller thumbnailcaches can make for faster loading times, but this depends upon your system and the state of the caches in the first place. I would only bother to do this if I've had a major clear out and got rid of a large amount of CC.

@simsample good point about crashing when I (re)-add many CC in one ago! Sometimes I have large CC download sprees between two plays. Now I was re-adding folders back to Downloads to check if I didn't exceed my max amount of OBJD.

Will keep you posted if removing thumbnails helps if I added many CCs in one go.

EDIT: fixed wrong username tag