I think there may be a few issues that the OP is seeing. This is a government hospital, Nagahama Municipal Kohoku Hospital, so it’s not a private hospital. However, there’s nowhere that states that possible Wayspots on government facilities are not allowed; this would be on a case by case basis.
Another part of this hospital is that there is also a nursing home, again not a location that is automatically ineligible, as well as a social welfare agency for the elderly. There certainly are Wayspots at places like these, and most do not interfere with the work of the facilities (I think both the residents, staff, and family/friends visiting could play at a Wayspot at an outdoor gazebo, for instance).
Being this is Japan, and there is a high resepect for the elderly, this may be one of the issues the OP is seeing with this Wayspot. However, just because some place may be for older people doesn’t automatically make it ineligible to have Wayspots. This could also be an area that is restricted, as I do see some signs on Street View that may indicate this, but that still doesn’t make anything ineligible, as Wayspots are allowed at places where people are restricted.
Personally, while this is just a green space in front of the complex, it may be hard to remove, since removal criteria can be strict. I have a hard time seeing this getting removed.
Here is the website for the hospital, if anyone if wanting more info:
I’m not finding a listing for an emergency department here, BTW.
The nursing home has a separate website here:
http://www.nagahama-shakyo.or.jp/ikanosato/
And if you want to take a look around Google Maps, you can do so here: