That would have been my recommendation as well. I'm thinking of cutting a door opening thru a concrete wall, and thinking about the “shovel and shut up” option.
I buried the entire concrete apron of a 16x32 in ground pool, plus the diving board in a couple holes at my old house. I broke it up with a jack hammer I rented from Home Depot. I paid a buddy with a backhoe about $250 cash for three hours of work with his machine.
I planted some spruce trees on top of the holes.
I had quotes of over $2500 to haul the material away.
Concrete is considered “clean fill”. There is nothing toxic about it. Just dig a deep enough hole so that it does not settle after you have filled the hole back in.
Or, rent a jack hammer and break it up into smaller pieces. That is what I did with the pool concrete.