Trust me, you aren't the first to wonder why the MoCo is clueless, on this issue as well as a ton of others. It would be pretty simple for Harley to just switch to a transmitter that could be easily programmed directly to the vast majority of door openers on the market, including those 20 year old simple systems. Perhaps if they actually installed door openers in all their bikes they would consider it, since it would be much cheaper than the transmitter/receiver system they have now. Since they only install them in the CVO Limited/Ultra models, they obviously don't consider the volume sufficient to justify the change. OR, they are just dumb as rocks.
Fix it the same way I did. Mount a remote for your garage door opener in your fairing and wire a pushbutton momentary switch to the contacts for the remote button. Locate the new switch on the dash or wherever you want it. In my case it works better and more reliably than the H-D system, at a longer range, and all I gave up was the high beam switch activation. I know some people have just put a regular remote in a fairing bin or windshield bag pocket, or the pocket of their riding jacket. It's not as handy that way, but it works and still beats getting off the bike to open the door or to close it when leaving.
JMHO - Jerry