The dynamic is different in the US. The US doesn't have national elections. All elections are run by each individually federated state. The national government of the US does not have the authority to override this.
If there was will in the US for a national ID, Congress and the powers that be could achieve this within a few years if they wanted.
The reason is the combination of:
1. The power to run elections was delegated to the states
2. States don't want to give up that power
3. The only way to change that would be for the states to vote to give up those powers
Yes, as you point out, not all federations are this way. Many others are missing #1 or #3 above. I pointed out that the US was a federation simply for legal context. As of course, local governments don't really have much power against the central government in a unitary state.
Democrats would be onboard with a free federally administered voting ID. Republicans wouldn't, though, because it's not about fraud, it's about making it more difficult to vote, because they lose when more people vote, and they literally said as much to the supreme court as a justification for their voter restrictions laws.
(they see it as "political party is not a protected class, so there is no legal prohibition from creating voter laws which are designed to disadvantage their political opponents")
https://www.nbcnews.com/politics/elections/supreme-court-gop...
There have been examples of this being gamed in the US. Gerrymander the county then force your political opponents into the least convenient polling place in the county.
This is the problem. In the US, there is no equivalent universal ID. Voter ID laws keep people out by requiring forms of ID that certain people tend not to have, e.g. requiring a driver's license, which immigrants and inner city residents might not have.
My dad who is a unicersity prof does not drive a car and does not have a driving license. Using driving license as a voter ID seems crazy to me.
Checks and balances of power is naturally inefficient, and tends to result in a more stable system.