I don´t wear any, same with bicycle. But my scooter definitely is not as fast as a bike. However, i do not consider my motorbike jacket protective equipment, because i only wear it when it is cold (also on foot, because slipping on ice sheets on sidewalks is a thing here).
If you are looking into something, i usually hurt my elbows and palms/hands/wrists before anything else. And knees. Bicycle helmet or so might be good. So, i would not necessarily look into one-fits-all, rather season appropriate gear, meaning: If it is to hot/sweaty so that you never wear it in real life, it is no good.
I have gloves with knuckle protection (with smartphone compatible tips, so that i actually use the gloves), which helped me out a bit. So, protectors over actual clothing might be good, but i am on the side of least stuff on me, which may not be the best position.