This is probably a problem with the hit testing, when dragging the element it doesn't find the root Grid and it returns the Page as parent of the new element, deleting everything else.

Don't see a problem with the hit test or anything in this video.
When you have a <Border><Rectangle/></Border> and try to drag an Ellipse into a Border, it'll replace the current content because Border can host only 1 child, so it can't be an additive operation.
This was done by design. The same thing applies to the Page (like in this clip), it can host only 1 element, so when you try to drag an element to it it'll replace the contents.

After reading your comment, I think the problem here is that when you attempt to do a similar operation in the Navigator (Like dragging an Element into a single-child Panel), we prevent you from doing this (red warning tooltip label). This prevents you from commiting a destruction action, and we basically make you intentionally clear the Panel's contents manually.
So my recommendation here would be to apply the exact same rules and mindset as it works in the Navigator:
1) Prevent you from dragging in an Element that makes a destructive replacement of what's already on-Stage/in the Navigator.
2) Accompany the mouse cursor, when attempting to do so, with the exact same red warning label as when you attempt to drag an Element into a single-child Panel.