In my day at my college to get summa cum laude you had to be recommended by your department (summa on your thesis or if the department didn’t require one some sort of A average), you had to have a certain GPA AND you had to have an A in a full year course in Social Science, Humanities AND a Natural Science. I came up one A short. There was no percentage limit, but I’d guess less than 50 students got summa cum laude. It took up a few lines on the program. There was a slightly smaller group of “magna cum laude with highest honors in their department” , a big group of magnas, and a very big group of cums which I believe required a B average.
The system is similar now - English honors determined by department Latin honors include the rest of your coursework, but Latin honors are now capped by percentage. 5% for summa, the next 15% for magna, then the next 20% can get cum laude.
I liked the fixed GPA better as you knew exactly what you had to do to get an A. I still kind of regret I didn’t take the extra Social Science course senior year. Though it would not have changed my life in any way except I’d know more about Japan the course I was thinking about taking. (I’d done very well in the China half of the course, so I’m pretty sure I’d have gotten the missing A.)
The short answer to your question is that 50% of the class at Harvard gets honors. I think that’s more than when I attended, but less than it had crept up to being before they put percentage limits on it.