Business is certainly getting better, and that is certainly putting pressure on First class (i.e. price differential not worth the incremental differences, which are often subtle).
The main advantages of First over Business are better facilities (both ground and air) and, more importantly, a smaller cabin (less people). Are those worth the price difference? Debatable.
The irony is that First class many, many years ago was like Business, in that it was luxury but served to quite a few people, viz. now the largest First cabins are about 14 passengers.
If carriers choose to keep it, then on the realisation that most may not pay the real money for it (and every blogger would tell you - without being comical - that you should never pay the money for First), First may remain as a marginal improvement on Business rather than a step up. BA is a rather good example of this. LH has been trying to define the step by accepting a suppressed standard for its Business class product, which is somehow still aligned against what they believe is acceptable to the Germanic market.
But look at the current carriers who are still set on keeping First. The Middle Eastern heavyweights are at least trying to keep First flying, culminating in what might be a huge p*****g contest. Qatar is watching from the sidelines whilst pushing ahead with it's "Business as good as First" strategy. The Asian contingent in at least Cathay Pacific, Singapore Airlines and Garuda may be nervous in maintaining First, but they are holding out with might and main. Whatever mainland Chinese airlines seem intent on keeping First might just be relying on a home market which will allow them to keep it, because on a world stage their products are not well acclaimed.
Between the European holdouts, the US-based ones and Qantas, it may just be a matter of running whatever First they have into the ground before it disappears. Keeping it may not be any sort of commercial benefit, but rather an image based one.
