The ADA does a lot of dumb stuff and rightfully gets a good amount of stick for it, but you have to remember that they are also having to optimize for a population that is overwhelmingly less educated and financially insolvent.

If you are educated and/or wealthy with diabetes[0], the odds are you have a good endocrinologist and/or are disciplined about diet and exercise. In these cases, given you're not an extreme case, your diet is largely based on consistency. It's not necessarily low or high carb diets (although the extremes obviously create complications), it's about keeping your insulin input consistent. This means you have to keep your "carb" (diabetes isn't all about carbs, but they are the biggest factor in your diet) to exercise ratio relatively consistent, so those that exercise a lot or have high metabolisms often still have high carb diets after diagnosis. The real killer with people who have the wherewithal to manage their diabetes is blood glucose swings, and the swings to the low end are quite a bit more dangerous than those to the high end. You have much less wiggle room for "lows"... using general numbers, a "healthy" blood glucose reading is ~120, a low is <60, and a "high" is >200. While that difference may seem small, a reading of 40 is much more dangerous than a reading of 220, as 40 presents a decent risk of loss of consciousness and other very serious, immediate complications while 220 may cause some long term damage if not controlled but mostly manifests as mental fatigue or irritability. To drive my point home, a reading of 400 is very bad, but quite fixable without professional medical help. A score of 30 or below is serious cause for an itchy 911 trigger finger, and might mean death if the patient has already lost consciousness.

All this is to say: Even in the best case, low carb diets are only for diabetics with a very good A1C and highly controlled and managed diet/exercise/insulin ratios.

Now consider that the vast majority of people with diabetes (see footnote again) are poor, genetically predisposed to obesity, and uneducated. Asking them to manage their diabetes in the first place is hard enough, much less asking them to make substantial lifestyle changes to eat healthily. These people are going to have high carb diets whether they like it or not. Given the dangers of lows on top of this, the responsible thing is to keep them consistent, recommend higher carb diets, and just hope you can help them manage their condition in other ways to the point of maybe not having limbs amputated, losing their sight, or dying at a middle age.

Most of all, though, this is a huge testament to how poorly we're taking care of the diabetes epidemic (yes, it's an epidemic) sweeping our nation. You can point to socio-economic issues, political issues, ecological issues, and so on, but the end result is we are abandoning and failing millions of people with a serious, chronic illness. Organizations like JDRF and the ADA do have serious problems, but at the end of the day they have very few avenues to actually affect change while the root causes still exist. Thus we end up managing symptoms and trying to minimize damage. Sad state all around.

[0] I'm going to blur the line a bit between Type 1 and 2 here. Of course, it's important to note that treatment and management varies wildly between the two but there are good general rules of thumb that apply to both, so i'll stick to those in order to make my point simpler