At least part of the cognitive system is lazy/avoidant, but it doesn't seem that test-takers consciously think "I'll just write down the first answer that comes to mind".

True, but it does tend -- if true -- to imply that the test-taker would have a desire of "minimize all extraneous functions".

Then, maybe solving the problem requires less effort once you have spent more time at reading the question.

My hypothesis here is that by making the font harder to read it's causing the test-takers to invest more cognition into properly reading the questions than their drive to "optimize" that labor to its bare minimum would otherwise imply.