I asked this same question not long ago and DOCGKR gave some good information. In my opinion soft armor backers need to be worn with issued SAPI/ESAPI. It's cheap insurance, and weighs next to nothing.
As far as people wearing their own kit, specifically airsoft garbage, the only thing cheaper than one troop, is two troops. I have never understood the desire to go cheap on a platform that is designed to be fought from and ultimately save your life. The AF has had a big prpblem with this as of late as well, specifically in Security Forces. The newer SF Airmen want to lose the IOTV and look like operators, but really have no idea of the "why" behind their kit. Most of those that go purchase their own get Condor, Rothco, TMC, etc. All absolute shit, and not worthy of a training environment, let alone a combat zone. I have been running our Training Section for around a year, and I've been able to get through to a number of people during our proficiency firing. I've been able to get my hands on excess sets of old, and damaged plates and twice a year I demonstrate the effects of at least our 9mm, 5.56, and 7.62, so people can understand the significant backface deformation and the need for soft armor protection behind the plates.
As far as COTS gear goes, I have pitched the idea up to Big AF to authorize, in writing, specific carrier/armor combinations that can be used for duty/combat use. Similar to the way a PD will have a list of authorized duty handguns that have been evaluated for duty use. I don't think it would take much work on a unit's part as most of the COTS PCs that are out there have already been evaluated for duty use, and are in service with a military unit somewhere already. For example, the LBT 6094, Mayflower APC, Crye JPC/AVS, etc. It would allow for more felxibility to meet unit/mission objectives, especially for a career field as diverse as Security Forces. Some units need heavy loadout for nuclear security, while others do airborne fly away security, and even more doing basic law enforcement, and static security. A "one size fits all" solution doesn't work. So, what i proposed, was to create the authorized list, and allow the troops to purchase their own PC/soft armor combination to be used with issued ESAPI/XSAPI plates and allow for the flexibility in mission sets, mobility, preference, agility, etc. Maybe too lofty a goal, but I think it is easily doable.
I can't begin to understand why guys don't want to wear the soft armor backers, especially when downrange. I understand it redeces weight, but it is negligible in my opinion.