Our North American beet pulp is a byproduct of the sugar beet industry, which is why it’s relatively cheap. The sugar is extracted and the pulp is left with only a faint sweetness. That’s why beet pulp is quite low in sugar/carbs. Sugar beets are large and yellowish.
Table beets are one of the high glycemic index root vegetables so if you used whole beets in feed it would be sweeter and also significantly higher in carbs. Table beets are typically red, but when I was buying veg boxes from a CSA farm, they had yellow beets. They liked fun colors, yellow tomatoes and blue potatoes.
Feeding root vegetables to livestock in winter is definitely a European thing, like mangelwurzels. I just went and Googled them, and they are also a beet. I thought they were a turnip like rutabaga which is also used as a feed crop.
Anyhow if you are putting human food in your feed products it will be more expensive than using a byproduct.
For me, the benefit of beet pulp and alfalfa cube mash is as a very palatable, relatively low carb, affordable carrier for VMS, salt, flax seed and extra water. Switching up to a pricier whole table beet product would defeat the purpose.