Ian, I think the "hole" left when playing traditional walking bass is, in great part, an essential element of that particular style.
I was lucky enough to see Jimmy Smith play with Jame Moody. On "Moody Blues", Smith was using a delightful foot bass line, leaving his left hand free for fantastic chord inversions.
I LOVE walking left hand bass...so lucky I get to play that style on a regular basis.
Russ