But if you want Software Engineers that will take up DevOps skills and responsibilities, surely you'd want to advertise this DevOps culture instead of a role? Advertising this as culture is likely to attract people that want to work in a place without a DevOps/SE stratification.

I think the only reason to advertise for it as a role, is when your tooling is too complex and you've given up looking for Software Engineers that could do it on the side. Which is fair enough, I guess, though providing a Golden Path nowadays is probably more popularly done by hiring Platform Engineers.