I love the driving analogy, it's quite fitting. Although I would argue that the analogy isn't complete. Knowing about mechanics would be very relevant if cars were not mass produced and you (or your small team) were building / modifying your own vehicle. Essentially, I think that most algos are not "off the shelf" standard yet, and they require a lot of building / fiddling.
In this scenario, only knowing about mechanics still wouldn't make you a great driver, but it would help you design a vehicle that works for you, and help identify vehicles that might blow up with you inside!
That having been said I use ML algos, and I suck at linear algebra. I often wish that my linear algebra classes hadn't been so dreadfully stale and boring.