But what about the air circulation. We could use materials that are resistant to fungus but IMO if the plants doesn't have adequate air circulation can't grow fast and healthy enclosed inside a box...

well these keikis are growing faster in a "box"
anyway I take the lid off every day. will transfer to reg pot when teh roots are longer/

Air circulation is a concern, but like Stefano I take the lid off every day and there is also a vent at the top.

Plants need oxygen and a completely sealed setup has never worked for me. This seemes to be working though, as it is getting a regular change of air.