For one thing I don't think most people would even agree on what foods count as processed and are bad. Some people are talking about everything except fresh vegetables, some people are talking about specifically industrially-processed food but would say the exact same recipe followed at home (minus a couple of preservatives) is perfectly fine, some people are specifically against fast food but might think canned foods are fine.
Large blood sugar spikes after a meal are what is bad for you, but this a more nuanced equation of things like glycemic load of the food (which is as much a factor of quantity eaten as it is glycemic index), genetics, and level of exercise. It's not as simple as just saying all processed food is always bad, for instance after a hard workout simple carbohydrates are not just ok but actively good for you, and ideally most people should be doing a hard workout multiple times per week. Some other components of processed food like excessive salt can be bad, as is the fact that they often push out more micronutrient-rich foods from your diet.
But it kind of strikes me as the abstinence-only approach to dietary advice. People love the taste of processed foods, I think we'd do better to encourage eating responsibly overall than insisting on avoiding processed foods altogether. And it's possible to be very healthy while eating a significant amount of processed foods.