Native speakers of English can pick up a lot of Greek and Latin etymology, even if they don't formally study Greek and Latin etymology (which is a pretty good idea, by the way) so that they can find many technical terms to be every bit that transparent.
How transparent is the term 車床 ? It doesn't mean "chassis," nor does it mean "flatbed of a pickup truck," nor anything else that a speaker of another language might guess. Some terms in any language are just plain arbitrary, even if they are made up of simpler morphemes.
I think you need to consider that the character 車 is far, far older than the automobile. If you think of what kind of bed a carriage would be on, it makes a bit more sense.
The real problem is that few people even know what a lathe is nowadays.
How transparent is the term 車床 ? It doesn't mean "chassis," nor does it mean "flatbed of a pickup truck," nor anything else that a speaker of another language might guess. Some terms in any language are just plain arbitrary, even if they are made up of simpler morphemes.