I've never seen people refer to beets in their list of veggies. I'm talking about plain cooked red beets, not Harvard beets or pickled beets (which are loaded with sugar)

They are anywhere from 6-8 gr carbs ECC for half a cup depending on the counter you use, or the brand for canned. It's high for people only on 20 or 30 gr carbs per day. But for people like me who have been able to up their carb levels to around 50, the numbers would make them an option and welcome change.

Is there a reason why we shouldn't eat them? Are they way up there on the Glycemic index?

I've had some this week in an amazing salad at a restaurant:
bed of mixed greens topped with beets, crumbled feta, onions, and drizzled with oil and vinegar. Last night I tried to reproduce that at home, adding a side of salmon fillet rolled up and stuffed with a mixture of shredded cheese, crumbled pork rinds and asparagus. I have a hankering for beets right now to help boost my daily veggie carbs.