> It's a very low bar to get over.
In theory but not always.
Not when corrupt officials with an agenda set up barriers (bureaucratic and otherwise) to obtaining ID's and registration, which disproportionately affect a class or population or area, especially one known to be different from the officials' preferred candidate or party.
Similarly, voting access itself should have very low barriers to entry, and yet there are instances where easy access (regardless of ID or registration etc.) has simply been removed, or diminished to drastic proportions; the removal of ballot boxes and polling places from areas seen as opponents by theoretically neutral but actually hostile and corrupt election officials, is an example.
So while it's true enough when you say "poor people and people of color manage to procure an ID", a caveat sometimes should be added: "in spite of agenda-driven people trying to prevent them".
Yes, if the system were allowed to work without interference, the methods and practices you describe would generally be pretty reasonable. But corruption and "gamesmanship" (to put it mildly) exist, and voter suppression is a real thing.