Note for our US-based friends, when we write First Class, it's actually First Class, not some marketing semantic for what should be called Business Class. 

Now that this is out of the way:

Waning customer interest in the costliest tickets prompted American Airlines to drop first class as it adds seats to its 47 long-haul Boeing Co. 777-200s. 

This is not a new trend. Companies like Air New Zealand, Turkish or South African have already done away with three-class aircrafts. Lufthansa or United are reducing the routes in which this configuration exists (maintaining it on very selected high-yielding ones only) . Not to mention those airlines that never truly had them, Virgin, Delta or KLM for instance. 

Reality is that the appearance of lie-flat seats have made Business Class more comfortable and exclusive. And corporates that used to pay First Class to their executives are either not doing it anymore or have moved fully private. After all, it can be quite costly:

A refundable, round-trip first-class ticket for a Chicago-Beijing trip departing tomorrow costs as much as $37,948, according to American’s website.