Now that I have middle of the night crabbiness out of my system, here's a real answer:
There is no monetary charge to get the vaccination. They are obtainable in almost every community. Depending on location, they can be obtained at almost any hour of the day or night (in the case of 24h pharmacy locations), and definitely outside of the time that a majority of Americans are at work during the day.
ID such as a driver's license or passport is not free. In most states you can get a free government issued ID. It requires several other documents to qualify for one. It requires proof of who you are, sure. Isn't that the point of an ID? It requires travel to receive one, sometimes involving leaving ones county in the case of several counties in Alabama's Black Belt. Most locations operate at the time a majority of Americans are at work and do not have flexible hours to accommodate them. If they can get to work, can they not get to the government building that issues ID'S?
I thoroughly expect my rationale to be picked apart; I had to stretch to think of why IDs would be difficult.