It doesn't have to be a 'free' city service. They just need to incorporate the cost as a fee when purchasing a new mattress. Other states do that. So every new mattress sold has already paid for the recycling of that mattress.

All mattresses are presumed to have been paid. Yes you can buy an old mattress, or move to the state with a mattress etc. But this way the cost is incorporated in the purchase and all mattresses can be accepted/picked up by recycling providers.