Oh, there's even a term for it! Thanks.Yes, the first reason (air flow) was the main if not the only one. We call it 'lang7-huang1' (huang1=hong1), 'lang7' is to put something in the "open" air.
Yes, I thought even more about it and arrived at the conclusion that "1" must be the *only* reason. Adding the mesh is actually labour intensive: the square hole has to be cut out of the wood, the mesh has to be laid in place, and then narrow little flat slats of wood have to be nailed all around the edge of the square hole, to keep the mesh in position. And the mesh can get torn, and then needs to be replaced, etc. So in fact, it would be much easier/cheaper just to use solid wood. In other words, mesh is only used where it is really needed, i.e. to allow the 'lang7-huang1', and certainly not because it's cheaper.
My instinct says that most city-bred TW people my age, native speakers included, would also say "chài". I've asked a few people my age how to say 小菜 "sióchài" in real Hoklo, but they'll sit and brood over it and get sidetracked. People born around 1976 or '77 and earlier speak much better Hoklo, tho. The drop-off is tremendous. Tâi-Hoâ Soàⁿténg has both kiâm and mi̍hphoè/mi̍hphè. Tâigí Pe̍h'oē Sió Sûtián has mi̍hphoè/mi̍hphè and indicates that mi̍h can be pronounced with either its running tone or its standing tone, depending on the variant. 