(...OK, just kidding everyone...calm down...)
As a veteran Im aware of the issues you note. My position is that if we can afford to bomb aspirin factories with million dollar bombs and if we can afford to execute "very small" strikes against Syria with cruise missiles costing 10s of millions then there is enough money laying around to to have both available to our troops along with the money necessary for them to qualify on more than one weapon. True, most troops simply don't require M16s. Then again, Im not the type to try to drive nails with a screwdriver. Different tools for different tasks. A sidearm isn't going to get in the way of latrine duty, weed n seed, or stirring oatmeal in the mess. I am proposing either/or for the majority of service members, most getting sidearms. Infantry, security, and similar troops should ALSO have a sidearm available along with their M16. Im aware of the issue of the weight of the total combat gear that infantry soldiers struggle with, they should still have the option to carry both.
As far as losing the weapon...all I have to say is that 18 year old Israeli girls seem to be able to find a place in their bikinis for their compacts during a day at the beach with their friends and still remember to not lose their rifle. I cant imagine why properly trained American troops on base shouldnt somehow be able to pull off a task as simple as not losing a sidearm in a latrine. (Place a hook near the handle for hanging the belt so that they have to reach past it to open the door. Im sure there is a contractor out there that should be able to produce them for only $37,000 per unit.)
Unless you were looking for "a section 8", I doubt you were standing up front using your .45 as a pointer for your unit to follow. I suspect the unfortunate reality is that he day an infantry officer "needs" to personally shoot someone in the field there should be plenty of M16s laying around for them to use. Maybe a marksman such as yourself should have been issued something more capable than the M16 all along, yet still have had the option to carry a sidearm. The rest of the days in your career you should have had access to a sidearm instead.
That's all probably true today, since we've been on a war footing for so many years, like the Israelis have since .... ummmm 1948. When I was on active duty in the 1980s, though, it was the Cold War and the troops were almost universally more scatter-brained. A buddy of mine, another platoon leader was doing a water crossing and one of his guys just lost an M60 machinegun (precursor to the M249 ? 7.62x51) into the Nisqually River. Just "OOPS!" Never recovered a belt fed weapon that was in pristine shape. I sometimes wondered if the kid went back on his own time with a scuba tank and made some great money on his "loss." Or if he did that and just kept it for a SHTF rainy day.