It makes sense. I'd only do an inch. I don't know the equipment, but think it's impressive your equipment will skim shallowly. Smart.

Several of my neighbors do this, often starting in January (if the soil is dry enough to plow) and replowing or rototilling every few weeks until planting time arrives. They seem happy with it, even though summer weeds eventually will sprout anyway. It does seems to keep the cool-season weeds under control by continually uprooting them soon after they sprout.

Dawn,
I plan to do this between crops too. Can you imagine 6 rows of PEPH peas 300 feet long?

Also, we have a bunch of middle school students growing sweet potato slips. We are planning for about 1600 slips. The kids will come back out the following school year to help harvest. We plan to use our mechanical potato harvester.
Johnny