The main problem with the first two sort orders is IMHO that the data points may not be there at all – for various reasons. So question is how to threat artists in such a case.
The third one is ambiguous* as users don’t add artists. So what to use as reference date? There might be situations where “Date Added” might not be what users expect. Also should this be added in the future, how to treat existing artist in a library as their “Date Added” might be missing at all because it wasn’t defined and thus stored in the past.
* Note: The Artists Browser contains only Primary Album Artists. There might be some hundred or thousands of artist in ones library that don’t show up (by now) in the browser but as they are there are also already added. Should a user later on add a album for such an artist, the “Date Added” might not reflect what the user expects.