First, I have been driving for over 40 years now and never in that entire time have I ever been told by anyone that backing in is the universal “right way to park”.
Second, if the parking structure is designed to have people park by pulling in nose-first then backing out then parking in that manner is the correct way for that particular location. Just as parking nose-to-tail is the correct way to park where there is parallel parking. You may argue that that is a poor way to design parking, but nonetheless if that was the intention then, as you note, attempting to do otherwise can result in difficulties you wouldn’t have otherwise.
It’s been the subject of endless debate, but the only actual benefit to nose-in anyone ever comes up with is that that’s the way they’ve always done it. Cars are more maneuverable with the wheels that steer out than in, and it’s safer to have a better view of the lane than of the parking spot.
I know I’m straying into IMHO territory, but there are certainly some relatively objective reasons to park nose in. In states where only rear license plates are required, many employers and parking facilities require you to park nose in so they can scan plates for parking violations. Also, and this is my experience, it’s a good thing to have back-up lights visible to pedestrians so they can tell you are actually in reverse and about to move. I’ve hesitated walking in front of many vehicles parked tail in that are running and have running lights on, but are just sitting there talking on their phones. You may not consider these to outweigh the benefits of parking tail in, but I feel that they are real and actual considerations.