Exactly; this idea that we HAVE to overwork our medical professionals is just outdated, and especially since COVID, actively detrimental to our healthcare systems.
Hire more people, pay them more, and give them time off so they don't burn out or get sick themselves.
Fun fact, the American Medical Association artificially limits the number of doctors that can go through residency programs each year. The limit is actually lower than the number of medical school graduates, forcing some small number of new doctors to leave the country because they aren't allowed to become licensed.
We should be aggressively recruiting and training folks to go into the medical professions, and paying for their training so you don't have to go into huge debt to become a doctor.
An overlap improves things slightly, but it isn't a magic solution. If it was that easy to transfer knowledge during an overlap, then they could also document that knowledge for the next shift without any overlap. And if your suggestion really just amounts to hiring more staff improves patient outcomes, I don't think anyone would disagree with you.