The article is right that generic "masks" don't work well enough to see the effect. But N95 respirator masks do and we should all be wearing them if indoors in public for long periods.

Well fit N95 (or better) respirators are needed in schools. Not just "masks". Unfortunately this does imply that very young children cannot be effectively masked because they will seriously degrade the protection by not maintining fit and seal. That is if the N95 respirator masks fit their small faces well enough to seal at all. This isn't an all or nothing issue though. Even a badly or intermittently fit N95 on a young childs face will protect more than a strap of cloth.

The CDC (and other institutions) not only failed on mask messaging, they actively told people the wrong things for months and then years. But it's pretty obvious from first principles. It's aerosol spread so you need to actually filter the air, not just block spittle.