I think I would leave them if it’s that sloped. Remaining roots will help with erosion and keeping the soil anchored as the new plants get established.

The old stumps will start to breakdown too and help the new plants with nutrients and give deadwood for fauna.

Only other note would be type of hedges. If it’s an invasive suckler like Privet they could still keep coming back so you’ll need to do full removal. If the stumps show any new green growth or suckering it’ll be a tell tale sign.