With Doctors the glove is the primary barrier for both the surgeon and the patient to prevent cross contamination, but gloves do fail and can be punctured during operations and a small number of pathogens do get on gloves. This is why they spend so much time scrubbing up, it is mostly in case of failure of the gloves.
From the NCBI (National Center for Biotechnology Information) website "The introduction of sterile gloves does not render surgical hand preparation unnecessary. Sterile gloves contribute to preventing surgical site contamination and reduce the risk of bloodborne pathogen transmission from patients to the surgical team. However, 18% (range: 5–82%) of gloves have tiny punctures after surgery, and more than 80% of cases go unnoticed by the surgeon. After two hours of surgery, 35% of all gloves demonstrate puncture, thus allowing water (hence also body fluids) to penetrate the gloves without using pressure. A recent trial demonstrated that punctured gloves double the risk of SSIs.
Surgical hand preparation should reduce the release of skin bacteria from the hands of the surgical team for the duration of the procedure in case of an unnoticed puncture of the surgical glove releasing bacteria to the open wound."
Do I trust the gloves of the workers while handling chickens (with sometimes protruding broken bones), no not entirely but gloves and bag together reduce the risk substantially as you point out. Also in the NCBI article it wasn't the only reason they scrub so much but because they have seen cross contamination even with still unused/sterile/unpunctured gloves. So best practice in a Supermarket should be wash hands and/or sterilse with alcohol, then glove, then bag, then dispose of those gloves, wash/sterilse hands then re glove with new pair for next process and so on. I doubt they do much of this because for a Supermarket time is money and so many may/will take the risk of contamination over the cost to their profits.