Olaes are great dressings that are very versatile but they don’t pack very small. If you really want to carry a trauma pressure dressing on your person I’d look for a simple ace bandage style one that is “flat” packed. Care under fire and tactical field care interventions are supposed to be quick and basic until care can be transferred to higher level and more equipped personnel.
If we’re looking to have stuff available for buddy aid, I
Get wanting to have more stuff, but our primary focus is to stop whatever threat caused the injuries first. A good med kit close by is golden.
If we’re talking self aid, we need to be realistic about the injuries we expect to be able to self treat and our ability to do so with that injury. Psychologically and physiologically, you're not gonna be great wound packing or wrapping a pressure dressing, especially one handed. How much of your own back can you see/ reach to accurately apply a chest seal to, etc.
Critical comms to the people coming to help you are arguably as or more important than significant ongoing attempts at self aid.