It still can cause problems, but the problems are usually not "I don't have a reasonable way to get to my new polling place" problems. They are "Can I fit a trip to the polling place in with my Tuesday schedule?" problems.
People in poor urban areas in cities with little public transportation are often actually much less mobile than people in rural areas. For them it is more likely to be a "I don't have a reasonable way to get to my new polling place" problem.
But the biggest reason closing polling places correlates well with hurting Democrats is that the people who decide which ones to close tend to pick ones that they will be more likely to hurt Democrats. E.g., from 2012 to 2018 Texas closed 542 polling places in the counties that had the biggest growth in Latino and Black populations (both of which are more likely to vote Democrat) and only 34 in counties with the least growth in those populations.
Please remember that this entire sub thread was precipitated from you saying that the mention of a reality TV star in the context of the effects of reality TV is too political and now you are actually discussing politics.