As a customer who was looking for a way to remove several items at once on Amazon when I came across this discussion, I think a very important point has been omitted. The answers here are theoretically correct if it were not for latency.
Consider this: it is removing 10 items and it takes approximately 1/10 per second to move and click on any button or box and your computer takes 1/2 second to reload a page (which is the case with each click of the Remove button on Amazon ). In option A, in total, it takes 1 second to click on the 10 delete buttons and 5 seconds to reload the page, which takes us 6 seconds to have our cart the way we want. In option B, it takes a total of 1.1 seconds to click on all your boxes (including the removal box after the 10 boxes next to your article) and after waiting .5 seconds to reload, I've only spent 1.6 seconds for my cart as I would like And what if I had an item? Well, I'm wasting the time it takes me to click on an additional button, but if I'm deleting two items, I've already recovered my time.
Now that I have made these numbers at the top of my head, maybe I can click faster, maybe click slower, maybe I have faster or slower Internet, but I can't just pretend that loading times don't exist. After all, the reason I came across this page was to find a way to relieve my frustration, and I must agree with your boss.
My suggestion: have a drop-down selector next to the quantity of the item that is purchased so you can adjust the amount of the item up or down to zero with an update cart button at the bottom. I don't know anything about creating a website, coding, etc. I am just a frustrated customer who clicks on the Delete buttons and expects the pages to reload.
I hope that helps!