Poll Taxes were designed to suppress voting by the poor. I think it is an oversimplification to say the poll tax was solely aimed at blacks even if it disproportionately impacted them.
The key is in your first paragraph. "Before the Civil War, only White landowners could vote." While you focused on "white", the more important word is "landowners". No doubt there were some white people that feared blacks would attain too much power, but just as concerning among wealthier whites was the fear that "white trash" (I use this term to describe how they, not I viewed poor white people) would gain political power.
Ever since the 1600s, the upper class of southern society feared the poor. Bacon's Rebellion suggests that the fear was not unwarranted. Indentured whites and "free" blacks had allied against the upper class.
In other words, the "elite" have often adopted political strategies in order to secure their political power. LBJ appears to echo that sentiment when he is quoted as saying...
These Negroes, they’re getting pretty uppity these days and that’s a problem for us since they’ve got something now, they never had before, the political pull to back up their uppityness. Now we’ve got to do something about this, we’ve got to give them a little something, just enough to quiet them down, not enough to make a difference."
In some respects, it appears that once the elite determined that they would not be able to suppress the "poor vote" (including blacks), they moved to a strategy of "giving them a little something" to keep blacks voting as the elite want them too. This strategy seems to be alive and well except it is not reserved to blacks.
What we need is not a government which goes around "giving people a little something to buy their vote". How often have you heard a politician promising "a little something".
What we need is a government focused at empowering the poor by making sure they have access to a good education in their urban and rural communities. A good education is not defined as teaching the right ideology but equipping young people with either the vocational skills and/or college education to escape poverty and realize the American Dream.
That education has to be supported by an economy that creates and preserves good paying jobs to raise people out of poverty. Instead, we seem to be falling back into the trap of teaching people to accept dependence on government as the "little something they are getting for voting as they should".
