The minimum age to use Itch is 13 years. Adding some kind of protection layer on top, to only show the k-12 items would be a curation task on the order of magnitude, that just making a new site entirely would be easier.
Each comment section on it's own would already violate k-12, as it is bascially barely supervised interaction with strangers on the internet. Also, there is no wallet or anything of the sort, that you can charge. There is not even a shopping basket. You cannot give your kids an allowance to spend on Itch. The customer needs to be legally able to enter the purchase contract. And those cannot be your kids, as they do not have a credit card or a paypal account, and it is not allowed to pay with someone else's credentials.
The target audience of Itch is not even 13-17 years old. It is people that are comfortable and capable of installing indie games and understand the risks and shortcomings of them. Risks and shortcomings include malware, badly programmed things, bad games, unfinished games, amateur developers and all sorts of quirks Itch has, that other sites do differently.
I think GameJolt tried to aim for that teen age group, but they radically changed a few years ago and I doubt they are suited for k-12. What Itch is rather good at, they do not do the aggressive advertisement thing, so often seen on pages.
If you seek a safeish environment for kids and video games, have a look at Scratch. Or, of course you can try the parental control features of a curated environment like Steam. Games on Itch are not curated. Apart from vague adult game separation, there is no age rating, not even a recommendation on Itch. Actually the most popular games are horror games. Which are unsuited for k-12.