I would love a way to do this! I feel like it wouldn't need to be paid for or a pebble sink personally. I think it's more of just a feature to make the activity more usable than one to make it more powerful so it shouldn't cost extra in my opinion. Plus there's already stoke in mining and I think it would be more confusing to have two pebble sinks for the same activity, especially since it wouldn't be consistent with the rest of the site.
I would like best if maybe there was a popup screen that like allowed me to select the amount of each metals I wanted to drop, say, 1 of 6 silver, or 3 of 3 copper, for example. But even just being able to drop them by type, say, all copper and silver but nothing else, or only drop all coppers, or drop all of the metals in the cart entirely if I wanted, etc. would be really helpful!
I don't like having to drop them manually because it's extremely inconvenient to do, and takes a long time and a lot of clicks, but also because I was saving up for a really long time for a den expansion at one point and accidentally upgraded my mining cart twice, keeping me from buying my new den tab for the longest time. The buttons are so close on my screen, and by the time I've hit drop copper ore and confirm so many times I kinda zone out tbh so I didn't notice I had hit expand instead of drop until it was too late. Which is my own fault to be fair but also it is realistically only a matter of time before I do this again given the current setup and I only really do mining to get moonstone shards, so it defeats the point of mining if my moonstones get eaten up by the expansions.
Another thing I have a problem with as things are is that I find the system of having to hover over a metal to get a popup screen and then click on it to be unreasonably difficult. I constantly miss the popup screen and have to start over with the hovering. And I have to do it so many times to empty my cart. I know I'm terrible at using the internet so maybe it's just me but also I feel this isn't the easiest to use system that we have currently. I just wish it had a better flow to it or something I guess.
So yeah basically I think this would be a huge improvement on mining to have an autodrop of some sort, especially one that lets you control which metals do and don't get dropped as well as the amount of each.