Unfortunately, that is not a feature that really exists in kiwitrees (or webtrees). I guess it could, but it is quite a complex problem. Similar to the “clippings cart”, but with a delete rather than download option. I might get a chance to look at it one day, but not soon.
However, there is a good solution that I have been using for many years. It involves downloading a fresh GEDCOM file exported from your site; use a simple tool on your local computer (see below) to remove the branch you want to delete; then re-import your tree back to kiwitrees.
The tool I use for this is “gedsplit”. It’s been around for years, but amazingly still works even on Windows 10 (not sure about Apple computers though). You can get a copy from the kiwitrees downloads page (https://kiwitrees.net/services/downloads/)
It certainly does work as delete. Did you download “gedsplit” and try it?
I have done what you describe as “delete the entire line” a few times on my own tree.
You select a person and the ancestors (or descendants, you choose), then you delete them and save the rest. Then import that back into kiwitrees. The import process deletes your old data, replacing it with the import which does not now include the ones you deleted.
But perhaps that is not what you mean by “delete the entire line”?