Rework of return ducting make sense?

My house has a mostly finished basement. We have an additional area of basement that we're looking to finish out as well. Ceiling height to floor joists above is a touch over 7 feet, which is great, but in the area we want to refinish the furnace air return drops that to about 6' 4". Still not bad, but less than ideal. The return duct goes from a floor register near the bottom of the stairs on the first floor above, across the ceiling of the area I want to refinish, about 4 feet or so and then through a brick wall to the furnace. Just before it enters the brick wall the duct opens up from 8 x 20 or so to 16 by 20.

Here's my idea... I'm thinking I can possible just remove the duct altogether. If I leave the floor register in place and put a grille across the opening as the duct goes through the brick wall, everything will look great. But will it work? The furnace would draw on the basement space rather than on the area at the base of the stairs on the floor above. It seems to me the basement space would naturally then just draw on the upstairs through that same grille and to some extent through the kitchen and down the stairs. Which to me seems totally fine. So what am I missing? Would this work?

Thanks,
J