Duplicate email types can be added in the web view, but you are not allowed to have duplicates in the DB view if that's how you have set up your business rules. DB view Business rules do not translate yet in the web view. I assume this goes for phone types as well.
This is important for data integrity. Also see https://renxt.ideas.aha.io/ideas/RENXT-I-1261
We are also having the same issue this needs to be resolved as it is creating issues with our integration with our edm platform.