1. People like business travelers or those with even minimal levels of status/benefits (who don't pay for checked luggage) don't usually preferentially check bags because luggage gets delayed, it's harder to switch flights when there's a weather etc. problem, and they have to wait at the luggage carousel.
2. Hard and hard-ish roll-aboards are a menace. Especially in a world of generally more casual dress, soft-side luggage would make overheads a lot more manageable--understanding that some people really can't use shoulder bags or backpacks.
At Copenhagen Airport, I usually get off the metro, walk to the luggage tag machines at the end of the platform and scan my passport (or boarding pass). That prints a bag tag (and boarding pass if requested), so after sticking that to my luggage I drop it off at the counter — I put the bag on the scale/conveyor, it scans the barcode, prompts me to press "Confirm" that there's no explosives etc, and I'm done.
I scan my boarding pass to go through the barrier into the security screening, walk to the gate, and very often scan the boarding pass again to get onto the jetbridge.
I can easily go from the metro to the plane without interacting with anyone. I understand this is Scandinavian bliss.
(Exceptions are trips to countries where I need my documents to be checked; e.g. to go to the USA a checkin agent has to see my ESTA visa waiver. Oddly, going somewhere like China which requires a printed visa in my passport does work on the machine, as the machine prompts me to scan it.)
I found American airports less hands-off (especially security, which is considerably more hands-on than I'm used to, "Sir, I will now rub your balls"). But then I'm almost always flying internationally out of the USA, so it's not a fair comparison against domestic (Schengen) flights in Europe.