A couple of loose, speculative reflections…
Prompted by LXNDR’s post on Leigh Brasington’s ‘Gradual training’ summary chart, (being intrigued to notice that the Brahmaviharas didn’t really feature in the list of selected suttas) I extended the chart to include the 11 suttas from the Majjhima that do include the Brahmaviharas.
MN7, 40, 43, 52 & 62 at least show that the Brahmaviharas can be part of a route that concludes with liberation. At the same time, the impression I started to get (remember, loose & speculative 
) was that the key function being promoted in connection to the practice was the overcoming of hostility and ill-will (although, if there is any stability in this idea, and if it is then coupled with the fetters/samyojana construct, and if that construct was understood as being sequential then the destruction of ill-will sould result in a person becoming “one due to reappear spontaneously [in the Pure Abodes] and there attain final Nibbāna without ever returning from that world”, MN64).
What stood out from the other suttas (setting aside 2 which had… ‘atypical narrative arrangements’) is that they seem to indicate that principally, Brahmavihara practice leads to the Deva realms, and MN83 & 97 appear to me to adopt a fairly disparaging tone towards the Brahmaviharas.
Either way, I’m a card-carrying member of the Brahmavihara fan club. 