When I hear outhouse, I think take a shit in a hole, just so happens to be a wood box around it.
I would still plumb a clean out for it. That way you can use it down the road for:
Another fancy brick British shithouse
A fancy outbuilding
Spot to clean out your main sewer line when it gets clogged with roots, condoms, wipes, tampons, etc.
A place to dump an RV or trailer grey and black water line.
But you do you. I wouldn’t bury it. I would, however, bury that supply line. I wouldn’t chance it having that freeze at some point. Dig down a foot or so, cut the supply, cap it. I don’t know what your supply is, but use a permanent fitting.
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