That's totally fine and safe in countries with high quality food and high standards of husbandry.

Nope, it's completely fine to eat cow or horse meat cooked like that (but not ovines, pigs or birds). It's very common in Italy. Never heard of food poisoning from this kind of meat. I do hear of food poisoning from chicken meat or seafood, though, as they are more prone to host dangerous parasites. I would still carefully select the meat vendor or restaurant, though.