Would capitalism without banks work?
Under most capitalism-like systems, companies are funded in two ways.  One is debt with positive interest, the other is by selling equity to shareholders.  If you could effectively prohibit debt, then companies could conceivably adapt by switching to a 100% equity model, in which individuals would shift all of their interest-bearing savings into shares.  This would create various inefficiencies (and create a lot of problems for consumers who would be unable to obtain mortgages), but wouldn't fundamentally destroy the incentive to produce.