It's impossible to use productivity modules in filtration plants? For quartz for example.

Productivity modules apply to the recipe, not the machine.
Maybe in this case it was an oversight, but imo productivity modules should not be overused(which they are currently) as they basically create resources (or mass) out of nowhere which contradicts the concept of resources itself. The concept of "resource" is imo that it can be used for profit, but it depletes eventually. Therefore I never understood those people who are adamantly for infinite oil wells or against non degenerating solar panels.
The "prospect-deplete-expand"-cycle is a core principle in any resource based game(mind factorio has already quasi infinite resources because of map-expansion, which also increases resource density)

Imo productivity modules actually need a nerf(less than 10%) and less recipes should enable them.
Espacially the ore enrichment process is very weird. First this recipe increases gain by +50%, then you get an additional 40% by productivity modules. It also creates water out of nowhere, so you have to burn the water in order to keep the ore enrichment going :D

The Idea behind productivity modules is that they are like efficiency modules for matter. You don't create resources out of nowhere, you just utilize your existing resources more effectively.

The reason why a lot of people are against the concept of very finite resources and decaying structures is because it creates a lot of busywork with little variety. They'd rather not spend 80% of their time building mining outposts.

Productivity modules apply to the recipe, not the machine.

Yes, and quartz is an intermediate product, so modules should be applied to this recipe.

They'd rather not spend 80% of their time building mining outposts.

You're right, developers even wrote about it in one of the FFF. In the late game, players spend most of their time building monotonous outposts and the game turns into a routine. I personally like how productivity modules are balanced, especially since level 3 modules themselves cost quite a lot of resources and time to produce.