I believe it's more of a generational thing.
Most people for example in their 40s and beyond prefer face to face.
Having said that I see you posted your question under the category of breaking up. I think it really depends on the individual/circumstances.
If for example it was a long distance relationship it makes very little sense to jump on a plane and fly somewhere just to end the relationship and fly back. A phone call or email might suffice.
Another scenario that might justify breaking up over the phone is someone has demonstrated a violent/explosive temper in the past.
In other instances where it wasn't a true relationship to begin with people oftentimes don't feel the need to have a "formal discussion".
An example might include having had a few dates with someone you've met online. They feel if we met online it's okay to end it online.
A person may have decided due to incompatibility it's not worth pursuing.
No one wants to believe their future ex would kill them and yet TV shows like 20/20 and Dateline along with the ID Channel are filled with such stories.
Breakups, layoffs, and firings are always done at the comfort level of the person ending things. If you're the one being dumped or let go there is never a "right time" to hear; "You're not the one!"
Whether you get that message face to face, over the phone, in an email or text the result is the same.
You simply don't have any say in "how" it's done.
Let it go and move on!