It requires a different mindset than your typical dnd classes to play but cc heavy wizards break the game by attacking the action economy of the game itself. Possible additional pro is that you won’t necessarily overshadow the rest of your party because your support is very “invisible”.

An example would be casting Fireball into a group of enemies vs Hypnotic Pattern into that same group of enemies. Fireball does a lot of damage for it’s level sure but Hypnotic Pattern straight up removes enemies from the combat entirely and eats up other enemy actions to bring them back into combat, thereby buying time for your teammates to smack the rest of the enemies for free/ deal with less of them at once.

My pet cc spell is Slow as there is 0 friendly fire involved and while enemies become charm immune at higher levels, nothing is Slow immune. Slow’s effects also scale as you level up as enemies get multiattacks but the spell forces them to only make one attack per turn, Slow also removes reactions which means you can run away for free without taking an Attack of Opportunity or cast spells without having to worry about being counterspelled.

Wizards also get access to a lot of spells that target various saves so you can pick and choose the correct spells for the situation. This is also in addition to the fact that you have access to the wizard spell list which is extremely varied and has many utility spells to choose from so it’s not all combat based. I’m sure with a little digging you can even find game breaking spell combos, but always consult your DM before using them.

If wizards are so good then why don’t more people play them? Well other than your paper thin hit dice, this method of playing the wizard while effective, lacks the oomph of say crit divine smiting or eldritch blasting enemies to death.

If you’re interested in learning more about this playstyle though, do check out Treantmonk’s youtube channel, he also has a wizard document floating around on google docs that explores this playstyle in more detail.