I'm sure we've had this discussion before so I'll make it brief, since you have no interest in absorbing my arguments anyway.
A lot of the problems are related to poverty, education, access and familiarity with computers (to easily find where to order source docs and to get them ordered online), time off, skill at navigating the system. Poor whites typically live in rural areas and have a DL, which is good ID. Poor blacks more often live in cities, do not drive and so do not have the required ID.
And put 600,000 (to use Texas numbers) of ANY demographic (white, black, hispanic, poor, middle class, wealthy), and especially 600k poor people with little education, access to computers etc and make them all get a new ID and I will guarantee you some small percent will not get it done, and some cannot get it done for various reasons. If 95% get the new ID, 30,000 did not. 99% means 6,000. Enough to swing an election? Possible and it beats a sharp stick in the eye and takes no time - just pass a law knowing some number of your opponents' voting base will not be able to vote next time!