Since 2014 airline CEO's have been saying First Class doesn't make any money. Attached are two articles - one from the AF CEO in 2014 and one from the AF CEO in NOV this year.
A couple quotes that spell out why F is important despite not being a money spinner:
'First Class was uneconomical because of the amount of space taken up by each seat and the level of personalised service required. It was retained as a "marketing tool" which is very important'. (M de Juniac. AF CEO 2014 - Times article)
'Experts say that, in status concious asian societies, first class remains an important service, but, elsewhere, the global financial crisis has killed the cabins profits'. (writer of same Times article.
'I don't see First Class becoming redundant, because there is a lot of value, especially if your airline does not have a long history. First Class can provide a lot of marketing and brand cache'. (Arthur Wu of Aviation consultants Teague - Telepgraph article.)
So there you have it - its biggest value is as a marketing tool. It is profitable in very few markets.
http://www.telegraph.co.uk/travel/ne...r-first-class/
https://www.businesstraveller.com/op...s-had-its-day/
https://www.thetimes.co.uk/article/a...ss-5k0bfl7j68w