A poll tax is illegal, so anything that adds to the cost of voting should be illegal. It's not just African-Americans, it's anyone that punches a time clock for a living.
Several of the states that have voter ID laws have made it much harder to get those ID's - limiting locations and the hours where they can be obtained. Not having an ID means not having a driver's license or a car, so when a state like Alabama closes all of the DMV offices in a county, getting an ID means the potential voter has to take a day time off of work, typically without pay, If your living at or close to the poverty line, giving up 20% of a week's income is a hefty penalty
It's also difficult for the elderly voters to get to such an ID - they can't run out of the nursing home and drive down tot eh DMV. On a personal note - it cost my family more than $300 to get my mother the ID she needed after a voter ID law passed in our state. She had not driven in years and had not seen her birth certificate in decades. And we are white.
Voter ID is also used to throttle the voting process itself . I've voted in every election since 1980, it never took me more than 20 minutes to vote until I moved to Virginia, which had a new voter ID law. There I had to stand in line for 4 hours to vote. The reason for that delay? The election official examining ID's would take several minutes studying each ID, slowing the line to a virtual standstill.
I've been in salaried positions for a long time, so all this cost me was a time, but while in line I was wondering how they expected someone with an hourly job to vote. What I found out later is that my precinct was largely Democratic, the Republicans did not want people there to be able to vote. Republican leaning precincts had no such delays, some areas that were mainly black had it much worse, taking as long as 8 hours to vote.