Try to let the soil/media dry out between waterings. I use yellow sticky traps and neem oil for plants I am going to eat. For ornamentals, I use Marathon 1%, shake a bit on the soil every 2 weeks or so.

Theoretically, shouldn't it be possible to create growing conditions which are filtered, i.e. no pests can enter the growing area?

Yes this is possible! Usually done with repurposed clean room pass thrus. It becomes harder to achieve as greenhouses get to 1+ acres in footprint.

Using pesticides is incompatible with selling fruits that grow from a rooted stick IMO. There is not enough time to respect legal safety intervals.

Neem oil