DAVx⁵
Short answer: Currently it's not possible (and if it would be possible, it may have unwanted side effects).
When you enter the base URL during DAVx⁵ login, DAVx⁵ retrieves related information from your server, including the home-set URLs, the actual calendar URLs, who they belong to (represented as an URL) and much more. So there's not only one URL to change, but many different URLs for different things.
Now when your base URL changes on the server, it means that all that information is not valid anymore. So everything has to be detected again, which means the whole setup process would have to run again. For DAVx⁵, the existing calendars didn't just change the URL, but "everything" changed.
Imagine that the URL changed because the server software changed – it means that URLs might have a different structure and even behave differently. For instance, the algorithm of calculating ETags may also have changed, which means that all data would have to be synchronized again and overwrite potential local changes.
The best current solution is to create a new account with the new URL and then delete the old account when the new account is ready and synchronized.
Attention: In the case that DAVx⁵ can't synchronize because your old URL isn't accessible anymore, there may be unsynchronized local changes (for instance, a new event). These changes will be gone when you delete the old account. Having a backup is always recommended.
We know that this is not a good solution, but this is a really complicated matter. (By the way, other clients like Thunderbird or Evolution don't let you change the URL even for a single calendar, too.)