This makes little sense.

Most airlines have the ability of mobile boarding passes, people can choose if they want to use their phone or whatever or print a paper one. They scan their phone at security and at the gate. So saying they will invest to make mobile boarding passes happen any time soon is just wrong, they have already invested the time and it is a reality on many airlines in many locations.

Luggage tags can never be paperless. They need to physically attach something to the bag so as it goes through the process the tag is read and it gets on the right plane and it's tracked. You don't need a copy of the tag on your device, as your device is not being checked.

You get a claim check when you hand a bag to somebody to check it in. Any other way, printing them ahead or whatever is ripe for fraud the only way to make sure a bag was checked is to tag it and give the proper receipt when it's accepted.

What you are suggesting would require them to somehow get you the reclaim check on your phone after you drop off your bags, and before they close the door of your flight and the phone has to be shut off. That isn't something I think they will want to spend any time with at all given that it's no extra thing for them to print the reclaim check, it's just at the bottom of the luggage tag. I think you are proposing a solution to a problem that nobody else considers an issue.