Where are you located, and what kind of grass do you have?

From my understanding, double digging helps avoid hard pan layer,
which helps root formation in some plants, and helps with soil
percolation. I agree this is the optimal way to do it, but it would
have to be a very small area to be worthwhile in my opinion.

On the ones I have done, I first killed the grass (especially if it
was bermuda) then tilled the existing soil, added 4" compost and
tilled again, then built the bed and added prepared soil mix that I
get in bulk to the proper depth. Dont know the scientific benefit of
this, but my thought was to have a soil transition instead of
definitive layers, which I thought would help prevent hard panning.

Good luck,
Bryan