The member has likely seen the pictures, yes. It is truly stunning. Constructing a root cellar is indeed a doomsday-like task that is not done in a jiffy. Personally, I would have thought twice before destroying it, as it can be used for so much, like wine, beer, apples, potatoes, and root vegetables. Good "second-hand value" as well, fortunately, it's a free country, fill it with filling masses if you're going to remove it.
The problem with meltwater in the spring is that there is a really large rock in the backyard that directs the water into the basement. We started using it for jam and juice when we moved there. We'll see, we have thought about tearing down what's above the stairs down because it's rotten...
The stone doesn’t conduct any water, so whether you plan to remove it, water will still come in anyway. The water probably drains somewhere so it doesn’t form a pool in the basement. As mentioned, fill with coarser crushed stone that lets water through. Some food cellars benefit from humidity; the only downside is that metal lids and canned goods rust if there is too much moisture. Otherwise, reconsider tearing it out.
Your problem is moisture and the wooden structure rotting. That problem won't disappear if you fill the basement with fill materials; the moisture will still be there, right? If you want to get rid of the water, you need to drain. But isn't this an old structure that has seen its best days and needs to be replaced? Keep the basement and renovate the outbuilding, oil the wood carefully, and ensure there is good air circulation.