I'd argue this point is nullified given recycling and trash live next to each other for pick-up (at least in the US). If your bins don't seal to keep scent away, they'll be targeting the trash cans anyways.
In parts of the world where clean drinking water is at a premium and increasingly more so, (like the western half and soon 2/3 of the US) it definitely matters to conserve the water we need to live whenever possible.
This brings up another good point though, packaging design should be changed to ensure the maximum amount of purchased product can be removed for use as easily as possible. So many containers today are designed to be sold as "this has 20oz in it!" and only 18oz is accessible. They then have tiny necks or convoluted lips or shapes to make reaching into the container with tools to remove the rest of the product difficult. The companies don't care about the loss of product as the extra 2oz costs them essentially nothing. Even though that added weight is wasting energy being transported at every single stage of the supply chain to be thrown away at the end, they got the sale because it said 20 instead of 18 on the bottle and they could mark up the price accordingly!
tl;dr on the last paragraph: If the container is designed to start its recycling journey as devoid of product as possible, the whole process will have less cleanup and energy/water use, whatever the process is.