What works more often is an explicit deposit, or a pay-for-return. I buy cleaning stuff from a local wholesaler who will pay a few dollars for each 20 litre container returned, a little more if it has a tap, and about $10 for a 200 litre drum (which I can also buy cleaned from a second hand drum dealer for $15).
But when you're talking about a 500ml dishwashing detergent bottle there's not enough value in the bottle to make it worth setting up a return and reuse system. If you get down into plastic bags it's complete nonsense, even for single-material (ie, non-food) bags at less than a cent each. In NSW we have a 10c fee per bag to discourage their use and even that is not enough to cover the cost of recovering and downcycling those bags (our downcycling scam just collapsed: https://www.abc.net.au/news/2022-11-17/recycle-collapse-proo...)
Look at the economics of milk bottle returns, for example. My parents pay ~10c/time to buy milk in glass bottles on top of the ~50c deposit on each bottle. People where they are do that because they intensely dislike plastic bottles and have the spare money to pay extra for milk.
There's actually a different reason they don't do it: Reusable containers make for a difficult business plan, because it's the reverse of a new-customer discount if you have to charge for the reusable container.
This makes it tough to, for example, start a takeaway using reusable stainless steel containers.