By all means photo ID cards existed in some way since the very early 20th century. However the ubiquity of ID cards for Americans didn't begin until the 1960s, with the invention of instant color photography by Polaroid in 1964.
Polaroid's invention was a clever but expensive breakthrough. It simply was too expensive for most consumers, and there was little chance of it becoming as popular as its instant black and white cameras.
In 1964, almost all states issued non-photo licenses, with the basic description of the individual (the height, weight, eye color info still found on licenses today) serving as the identifier of the driver. (The two exceptions were California and Colorado, which issued black and white photo licenses, with Polaroid equipment.)
But Polaroid saw an opportunity, and began aggressively lobbying state legislatures: color photo licenses meant "better identification." Citizens shouldn't worry about having to bring their photos in, so the state should take the photos at the DMV. And ideally, issuance would occur immediately, so the driver walked out of the DMV the same day with their color photo license.
Ironically black and white photographs are better for identification, as the features of the face pop out better than they do in black and white. While it's true that citizens didn't have to worry about bringing in their photos if the state took the photo, it also meant that citizens were often not happy with the results because they couldn't select a photograph that they liked. And while immediate issuance was convenient, instant technology was a lot more expensive than taking a shot on film that needed to be developed, and mailing the license home to the driver.
Nevertheless almost all states bought into all three requirements of the Polaroid model and the company created a lucrative market for themselves and their color instant technology. Most states issued color photo licenses by 1975. Almost all states did by 1980, and Polaroid was the vendor in at least 2/3rds of the states.
Surprising to us today, the historical record shows that license fraud wasn't a problem with the non-photo licenses. The identification information was really only good enough to ensure that someone didn't use a random license for ID that they picked up off the sidewalk. It wasn't trusted all on its own for much more than that, and besides, we didn't use them for ID anyway, so having a counterfeit one or someone else's wasn't all that useful. Polaroid said the color photo licenses provided for "better identification" but in my research I never found any citation of fraud. It was actually unimaginable to the people of that time.
ID card fraud happened almost immediately after the photo was added. The photo license became a trusted, universally accepted document, and uses for that document started to appear. Once that occurred there became an incentive to have a fraudulent document.
The main incentive for fraud was (and still is) underage drinking. Photo licenses enabled states to strictly enforce minimum age to drink laws (the national 21 year old drinking age could not have occurred without nearly ubiquitous photo ID, it's no surprise that it appeared in 1984, a few years after almost all states had photo ID.) Before photo ID, drinking age enforcement was loose and approximate. After photo ID, alcohol could be denied to a 20 year old just one hour before they officially turn 21. That's a level of micromanagement which we are now accustomed that would have seemed ridiculous and absurd to most of humanity.
Considering the fact that the strictly enforced 21 year old drinking age was probably the biggest change to happen because of photo licenses, it's funny to note that it wasn't a use for photo licenses that Polaroid dreamt up when they lobbied state legislatures to require color photographs on licenses.
Of course Polaroid didn't foresee fraud problems with their color ID cards either. It is ironic to think that ID fraud didn't really begin until the ID became a photo ID. But it's particularly ironic that the fraud problem became so lucrative for the people who caused it--Polaroid. Fraud meant that states needed to be continuously updating their equipment in order to make more difficult to counterfeit ID cards. The cards are however too ubiquitous to go long without being counterfeited, so the counterfeit-upgrade-counterfeit-upgrade cycle happens quite quickly, and it's happening even faster now, because counterfeiters are becoming more and more sophisticated. The only winners of this un-winnable war against license fraud are the ID making companies, who are constantly upgrading ID cards which will be outdated in just a couple of years. The fact that people don't realize that they are selling an inherently defective product is a tragedy.