If the stump is solid and no rot then I don't see why you couldn't lag screw into it and put a post mount bracket on it. I'd cut the stump above grade a bit and pitch cut it so it deflected water away from the lag screw. Worst case is it loses some stability over time and you do something else.
Removing stumps sucks and close to the house I'd be digging it out and cutting off roots before pulling it just to be sure I'm not damaging foundation/footing/utilities.
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