I'm not sure the cost of privately held false beliefs is as low as you think it is. The universe is heavily Causally Entangled. Now even if in your example, the shape of the earth isn't causally entangled with anything our mechanic cares about, that doesn't get you off the hook. A false belief can shoot you in the foot in at least two ways. First, you might explicitly use it to reason about the value of some other variable in your causal graph. Second, your intuition might draw on it as an analogy when you are reasoning about something else.

If our car mechanic thinks his planet is a disc supported atop an infinite pile of turtles, when this is in fact not the case, then isn't he more likely to conclude that other things which he may actually come into more interaction with (such as a complex device embedded inside a car which could be understood by our mechanic, if he took it apart and then took the pieces apart about five times) might also be "turtles all the way down"? If I actually lived on a disc on top of infinitely many turtles, then I would be nowhere near as reluctant to conclude that I had a genuine fractal device on my hands. If I actually lived in a world which was turtles all the way down, I would also be much more disturbed by paradoxes involving backward supertasks.

To sum up: False beliefs don't contaminate your belief pool via the real links in the causal network in reality; they contaminate your belief pool via the associations in your mind.