With regards to the just moving a card, we've set up the pipeline so at each stage certain fields are required which makes updating more involved that adding notes to a deal which is often forgotten, the added upside of this is it enables us to do cohort analysis and report back on conversion rates post certain objections, problems that led to the highest conversion etc.
With regards to the deal surgery it is usually held by our Head of Sales or if he is away, held by me, but in situations where the founder is a rep I found it can be really useful to have it hosted round robin, it keeps everyone honest and stops a "Me against them" culture.
Monday Surgery is split amongst Head of Sales, 3 AEs and 4 BDRs.