This reminds me of how all the city e-scooters are treated. Those rented by people with apps are treated terribly and thrown around like trash by their operators. Those actually owned by people are treated very well. At it's core it's basically a strong argument in support of private property (at least in this instance).
I would love it if you could solve this sort of social issue, but I wouldn't underestimate the difficulty of doing so. Successfully making people feel responsible for shared tools is almost equivalent to "building a better society". It's a worthy goal, but people have been trying to do so for basically all of human history.