The idea of voter ID is fine. The problem in the US is the implementation. Those other countries have national ID systems and are good at making sure everyone gets an ID.
In the US there is no national ID. There are state IDs but a significant number of eligible voters do not have one and many cannot afford to get one. Even if there is no direct fee to get an ID it can cost a lot (sometimes over $100) to get the documentation needed. It is made more difficult and expensive by the patchwork record keeping in many states, which can require searching in many different counties for birth records for example if you aren't sure exactly where you were born. I think most states do have statewide record keeping now, but some have not gone through the old per county paper only records and scanned them and added them to the central system.
Worse, some states seem to have deliberately tried to make it harder for people who are likely to vote against the party that is making the rules to get IDs and easier for voters who are likely to vote for them to get IDs.
For example, under the guise of trying to save money they close down many of the offices that issue IDs. These closures mostly are in areas where groups more likely to be against that party live, often poor and/or minority areas. This sometimes leaves those areas with no place to get ID within 50 miles, which can be difficult for people in poor areas with no affordable public transit and low car ownership.
Another thing is picking what ID is acceptable. Say make hunting licenses acceptable as ID, but do not allow student IDs from state colleges.
Make an ID law that includes funding to pay for getting IDs for those who do not have them, including assistance and funding to find the required records, and that sets up a system to make sure that going forward new citizens get issues acceptable ID, and finally that has a way to grandfather in people who can show by clear and convincing evidence that they are eligible to vote and cannot reasonably obtain an ID, and most people who object will drop their objections.
Here's a whole bunch of links about this.
https://www.projectvote.org/wp-content/uploads/2015/06/AMERI...
https://www.politifact.com/factchecks/2012/jul/11/eric-holde...
https://www.aclu.org/documents/oppose-voter-id-legislation-f...
https://www.usccr.gov/files/pubs/2018/Minority_Voting_Access...
https://www.washingtonpost.com/politics/courts_law/getting-a...
https://www.vox.com/xpress/2014/11/4/7157037/us-voter-id-req...
https://www.npr.org/2018/09/07/644648955/for-older-voters-ge...
https://rewirenewsgroup.com/2014/10/16/well-actually-pretty-...
https://www.theregreview.org/2019/01/08/shapiro-moran-burden...
https://www.theatlantic.com/politics/archive/2014/10/heres-h...
https://scholars.org/contribution/high-cost-free-photo-voter...
https://now.tufts.edu/2018/01/23/proving-voter-id-laws-discr...
https://www.brennancenter.org/our-work/analysis-opinion/debu...