I believe that in Greece — as in most countries where photo ID is required — that ID is provided free of charge by the government, without inconvenience to the person receiving it.
Here in the US, there are considerably more hoops to jump through, and these hoops are more difficult for the poor and the elderly. These difficulties range from DMV offices being inconveniently located, DMV offices only being open during times when most people are working, and not everyone can take time off their job, fees needed to obtain birth certificates or other documents, etc. Which is, of course, the whole idea behind voter ID laws — they’re meant to disenfranchise people. Apparently you didn’t read the multiple accounts of Republicans gloating over how these laws were going to help them win elections. There’s your reason for them.
And your examples of Democratic corruption — do you have anything that isn’t well over half a century old?
We already have ID for our voters. It’s called a voter registration card, and they are issued to every registered voter in all but a couple of states. These cards have the name of the voter (exactly as it appears on the voter rolls), the address of the voter (exactly as it appears on the voter rolls), the precinct where the voter is supposed to vote, the political party of the voter (in most states), and the signature of the voter, which is supposed to match the signature the BofE has on file. These cards are free, and they’re mailed to the address of the registrant, so there is no expense or inconvenience to the voter.
You would think that if voter fraud by impersonation is such a huge freaking problem, the very first logical thing to do is to ask voters to produce these cards at the polls. After all, every voter has one. But that doesn’t help Republicans, does it? No, they have to come up with something that will make it harder for certain voters to vote.
Perhaps if our government took a photo of the registrant at the time of the registration and then added the photo to the voter registration card that gets mailed to the registrant, this would fulfill the requirement of a government-issued photo ID, and it wouldn’t cost the registrant anything, nor inconvenience them unnecessarily. But I don’t look for that to happen, because that goes against the GOP objective of disenfranchising Democrats. And it’s been well-established that’s the reason for these laws.