Factoid: When I went from inactive reserve right after graduation to active duty status, the official term was "Extended Active Duty", or EAD. That means I was full-time active duty, as opposed to the normal reservists who were active for a given period, such as monthly training.
While active, the part-time reservists were allowed to use the BX/PX, commissary, concessions, Class VI package stores, etc. They had to show a reservist ID card and their orders placing them on temporary active duty. For the duration of those orders, they had the same access to military "perks" as those on full-time status.
I'm not sure about medical unless it was for an injury that occurred during training.
Reservists also qualify for other benefits, like tuition assistance and VA mortgage guarantees. They also accrue retirement points. I worked with a guy who was a civilian GS employee at HQ PACIFIC FLEET. He'd retired from the Navy as a Lt Commander IIRC, bought into his civilian retirement (not sure how that works -- somehow it reduces the double-dipping and lets you retire with more benefits on the civilian job side), and he retired from the reserves a couple of years before retiring from his GS job. I think his reserve rank was Captain/O-6. Added up, he has an active duty pension, a reserve pension, a civilian government pension, and Social Security. That also includes all the medical and base facility access all military retirees enjoy (yeah, he's bottom of the queue behind active duty when going to a base hospital, but it's better than nothing).
How do you get people to join the reserves? You have to entice them with tangible benefits. So, even if we went all-volunteer, mostly-reserve forces, the cost would be reduced, but not eliminated. Annual payroll expense would be much lower. One of the ways the reserve forces are kept at needed levels is by requiring reserve service when the active duty hitch is up. For example, my ROTC commission required a 4-year active duty commitment, and 2 years in the reserves. For each professional development course I took (Squadron Officer's School, college classes on tuition assistance, etc.), I had to commit to an additional length of time either active duty or reserve. Nothing's free.
I was a little lucky in that the Clinton Reduction in Force included a forgiveness of certain service commitments for people voluntarily separating. I received a severance lump sum of about $40,000 for my 9.5 years of active duty service, and all the leave I'd saved was paid out to the tune of about $12,000. And the service commitments I had from the college courses I'd taken over the preceding 2 years were erased. Since I was active duty for less than 10 years, I decided another 10+ wasn't going to be better than a contractor job. Also, the major's promotion board had been delayed for the 3rd time, meaning my next promotion would be at least 9 years after I pinned on Captain/O-3 -- nothing said they wouldn't bump it again and again. Before the delays, I expected to be a Captain for no more than 6 years +/- 1. The writing was on the wall, so I volunteered to be kicked out!

I never once regretted it. I've traveled more, contributed more to the military of all branches, and been treated better than I ever would have if I'd been promoted to Major and above. I was able to continue being the technical lead rather than being the guy in charge of the organization.
Anyway, I think the pendulum swings between active duty military and civilian/reservist position-fillers every few years. Seems like we spend more money than we save each time we switch "solutions."