You can not and should not get a reclaim check until you hand over your bags.
You can though - at self-check-ins in (for example this year) Norway and NZ, I can state I have one checked bag , get the printed-out baggage tag c/w tear-off reclaim check at a kiosk ... but then don't take anything to the bag drop.
However, I'd assume that the lack of a matching bagtag being scanned after the bag drop would scupper my claim for lost baggage, since the airline would have no corroborating proof of having ever received it.
My main gripe against sticky claim checks on my passport is that at some point I put my reading glasses in the same shirt pocket as my passport and the lenses get smeared with the sticky stuff.
I have the Qantas electronic tags as well, saves a bit of time at Aus domestic check in.
Mobile apps would be an improvement I guess, if only to my phone company's revenue with even more roaming data charges. I'd also need chargers at the baggage services desk so I could power up my phone after I've left it on accidentally for 12 hours, so I could claim my missing baggage.