Well if we go by canon then including those without specific citation then the wizarding world only has about 316 spells total using the full wiki list, of which, 15 which are medical in nature. Of those 15, 3 of them cure a specific minor ailment.
I see you ignored the rest of my post about the fanon.
Compulsion Charms were invented by fanon for the purporse of bashing. And if you go with all the fanon Harry Potter fanfiction has come up with you end up with a completely different mechanical universe.
If Compulsion Charms existed, then do you think nobody would have used them and been pointed out to have used them in the books? If Compulsion Charms were so useful then why would people use the Imperius Curse? You know, instead of these spells which work better and yet are somehow legal? Infatuation Charms would lead to Love Potions being obsolete and not existing in the books.
In Book 6 for example, if Compulsion and Infatuation Charms existed ... then why wouldn't they been thrown around like confetti by the girls who wanted to be Harry's Girlfriend? And why would Hermione use the Confundus Charm on Cormac McLaggen in sixth year when the Quidditch Tryouts were happening? If there was something better than a Confundus Charm which would be less suspicious then why wouldn't it be used?
And during Book 7, there are countless places on both sides where Compulsion Charms instead of the Imperius Curse would habe been useful.
There is a difference between writing Harry Potter Fanfiction and Harry Potter Fanon Fanfiction, the Plotholes Fanon brings in make the setting even worse. If the fanon was true, then why would any of the plot in the books ever happen? Can you, if we admit just existence of The Compulsion Charm, how different the First Wizarding War would have been?
Would the Ministry have not fallen if Voldemort and his Death Eaters had Compulsion Charms in the first war too?
Please, don't start following the fanon which makes the plot of the books even more nonsensical. The Fanon introduces more plotholes than it fixes because it's nonsense.
To use the example of the fanon charm of the Notice-Me-Not Charm (Which if I remember correctly was invented to hide Snape being pregnant in a fic which is already a do-not-use reason to start with) why would you need an Invisibility Cloak if you can basically go Imp on the setting? It's not like The Magical World has CCTV Cameras.
The fanon at this point is complete nonsense. Which at least the OP is doing the research into Half Blood Prince even if it's causing some issues with how they're having to deal with Rowling's nonsense.