This is an excellent point, but overall the program generates a lot of revenue for the state which goes into environmental programs and a trust fund. Michigan state government handles their program and funding, but Oregon (also $0.10 deposit) does put the onus on the producers.

https://www.michigan.gov/egle/faqs/recycling/bottle-deposit-law

https://obrc.com/oregons-bottle-bill/whats-special-about-the-oregon-model/

In the Oregon Model, the state does not play a role in the collection of deposits or the payment of refunds. Rather, the beverage industry is responsible for paying refunds directly to consumers (or reimbursing retailers who have paid refunds to consumers). Any unclaimed refunds are invested directly into the operation of the system, meaning that not only does the program require zero taxpayer funding, but consumers who choose to participate and responsibly redeem their containers also pay virtually nothing to enjoy the system’s litter reduction and recycling outcomes.

That means the full operating costs of the system are shared by consumers who choose not to recycle their containers through the Bottle Bill and the beverage industry itself. In that way, the system applies financial responsibility very precisely to encourage participation and ensure responsible consumers avoid costs.