Nurses do actually end up spending more time with patients, it's just that they spend more time with rich patients.
The actual, tangible form this is taking right now is concierge medicine, home health aids, private practice, etc. My wife's (very good) ob-gyn had enough of working in institutionalized medicine where she's paid about what a L4 FANG engineer makes and pretty much has to follow the script that the health-care system dictates, and quit. Now she does perimenopause consultations for FANG execs at $1200/hour.
My uphill neighbors are in their 90s. I think the wife was in VC or something back in the 70s and 80s. There's a steady stream of nurses and home health aids up to their property. Seems like they've got a full care team working out of their home.
Across industry and industry, we see the same pattern. The mass-market product gets cheaper and less labor intensive, at the expense of any human touch. Everybody displaced, if they're any good and wants to stay in the field, moves up-market to do custom professional services for rich people. They pay for it, because if you want people to do good work for you, you have to pay them more than they can get otherwise.
This has a surprisingly easy solution: get rid of the rich. It's never, in the history of the world, been in anyone's favor, except the oligarchy, to privatize everything.