At what rank should Soldiers be exempt from organized PT?

Rank, never. However, I understand that some duty positions and the responsibilities involved will not allow participation in organized PT during the "prescribed time"...such as foodservice soldiers preparing breakfast and hospital soldiers. In MY case when I was a Family Readiness Liaison, I had certain AM missions to acquire free supplies for my unit that I was required to pick up myself. I had to drive all over the state to get this stuff, so I had to start as early as possible to get done as soon as possible...which would keep me from organized PT. IT DID NOT, HOWEVER, keep me from doing PT on my own.

Retired

When they are retired, not before.

Never

Basically any and all PT is necessary to maintain your ability to perform to the level required.
In my active duty unit we did various forms of PT to maintain our conditioning. When I was in the Guard, we were on our own but the unit worked out a deal with the local training center for us to have available the various exercise programs and equipment. My unit was subject to a PT test at any time during drill. We didn't do a PT test every month but must be ready to do one if required. That way we were to assure ourselves that we didn't "slack" on our conditioning.
So basically, to answer your question is that we no longer need to have any organized PT at retirement.

None. Although you can otp out of the APFT at age 60 and above.

Death.

AS a old old retiree I think it should be broken down into age groups.Everyone needs to keep in shape as best as they can..A 35-40 year old can not keep up with a 18-20 year old..PT should be modified to fit age groups..I have been through the PT in the Marines and later in the USAF.Half way through my USAF time I could never keep up with what I did in my younger years..

Unit PT is a joke sometimes, honestly I’m a firm believer that you should be able to do pt on your own and be accountable for yourself mess around fail a couple pt tests and you should be gone

No Rank Is Exempt, the only day you will be exempt is the day before you retire.