I am not sure I do.
So we give it a new name now then in a couple of years have to give it another new name. There is no stability.
To call it Tyrrhenian Flycatcher now means that if the split happens we can take off Balearic Flycatcher and have just one more new name change. That is what I would like to see happen anyway.
Vermilion Flycatcher has been spilt into four - Vermilion, Scarlet (which by the way it isn't) Darwin's and San Cristobal (extinct). They haven't changed 'Vermilion', despite the scientific name change, as it keeps stability.
B
There is a similarity between the Vermilion example you mention and the spfl: the majority of the latter still is called Spotted Flycatcher because that name still encompass the large majority of the birds that were included under the old concept.
In a future split of Med Fly, the split would be much more down the middle, and therefore, keeping the name for one half would be much less appropriate. The stability you want is found in the scientific name. So, I think we have to agree to disagree.
Niels