Sounds like you've been doing some homework.... keep up the good work! If you are not familiar with API RP-520 Parts I and II, you will eventually want to look at them as they are a good reference covering the mechanical operation and sizing equations associated with relief devices and considerations for their associated piping.
Regarding whether every vessel should have a relief valve, pressure relief device requirements are usually associated with the Code or Standards to which the vessel is built. Local governing authorities (local city, your plant, etc.) may have additional requirements. So we need to backup a bit and you need to determine what code was used for your tank.
ASME Section VIII is a common pressure vessel code in the US but you need to confirm if it applies in your case. API 520 and 521 are intended as supplements to ASME Section VIII.
But let's assume that ASME Section VIII applies, then you may want to get this reference which includes excerpts from ASME Section VIII as well as being a good relief valve reference in general...
Now look at UG-125a and UG-125g...ASME says a relief device is required for all pressure vessels following ASME Section VIII but accepts that the relief device does not have to be installed directly on the vessel. Similar language can be found in API 521....look in the appendix section that covers Special System Design Considerations where they discuss having a single relief valve protecting several pieces of equipment.
One thing you may want to double check is your claim that the plant air is below MAWP. The normal operating pressure of the plant air system may be below MAWP but what regulates or limits the maximum pressure for the plant air, is it a relief valve and is it set at or below MAWP of your air tank?