I think this trap is rarer than you would think. I qualified for Pell Grant but still had no problem arranging transport to testing.
I can think of all of my friends who couldn't be assed to go to the test or ask for voucher, but I couldn't imagine them being academically successful in college anyway.
Not at all. You can’t design the standard system used for everyone around the needs of people in extreme circumstances. In the US, 80% of even poor households have access to a car. Likewise, the $55 one-time registration fee for the SAT is not unaffordable for the vast majority of poor people.
The percentage of even poor families for whom these are the barriers to taking standardized tests is small enough where you can just have the regular system and come up with special case accommodations for kids who are truly desperate.
I can think of all of my friends who couldn't be assed to go to the test or ask for voucher, but I couldn't imagine them being academically successful in college anyway.