Well, I am truly sorry that ASA has such a low expectation and tolerance of ineptitude in their ramp/gate employees. I am now in agreement with you! Put you bags in the cabin and let the paying pax have the lost bags. Again, please tell your management thanks for all the effort they put into the betterment of the fractional industry.
A side story, if you will, that goes nicely with yours. Airline in to OMA on ASA. Wait in the jetbridge for bag. All bags are gone and I am still there. Agent very forcefully explains to me that all the carryons are unloaded. I suggested that they were not. I was then informed that I had checked my bag and that it would be at baggage claim. I explained that it looked like the "real" pilots' bags and I had physically placed it on the cart in the rain in ATL. He mumbled something about baggage claim again. I went to the ticket counter downstairs and found a more than competent and way less methed out Frontier agent who gladly took my $20 to go look for and retrieve my bag from one of DL's Canadairs. He and I chuckled about it. I then got in a cab for the hotel, single bag for a 7 day with a clean shirt for every day and some play clothes, in tow.
We used to personally place our overnight bags into very large high-visibility yellow vinyl bags which would Velcro shut and place them in the cargo bins ourselves. You couldn't miss these things. The rampers would then remove from the airplane, struggle to get them out of the yellow "crew bags", and send them to baggace claim, another airport, etc... They of course would say "what bag?