dont know if that would work so well . besides getting air, you also want the outer material to get mixed in good.
my compost corner is about 15x15'ish . when i make a big heap it can take up about the entire area with just enough room to walk around it easily.
that doesnt leave room to flip the pile back and forth, so i've employed my rotor tiller for that task (the only job it has anymore). till it down flat
then heap it back up with a pitch fork. works great! and cuts the job in half.
not the most permaculturally-aligned of solutions, but it works .
i can also speak to some of those barrel tumblers.
i had 2 small ones that were given to us, they worked better as an outdoor vermicomposter than for hot composting.
they were just way too small to generate good heat quickly. maybe 20gallon size or so.
even the 55gallon ones are pretty small in my opinion to get good heat...i've talked to owners of them who report the same experience.
may be fine in the city with zero room for a pile(thats where mine live now) but take forever.
now what they WOULD be good for is as a compost trommel .. or simply build one from wood and hardware cloth like this.