I'm sure there's all sort of business lessons we could learn here. Among them that an early lead doesn't always lead to lasting success. AIM federated with Apple iChat, Facebook Messenger, and Google Talk, as well as ICQ after they purchased it over the years, but that didn't turn into anything lasting either.
It's probably my bias from working at WhatsApp; but I don't think they did a great job working with mobile, and that combined with lack of support from management killed them when smartphones took over the mobile market. They did have some support for AIM on feature phones, but I think it was all based on SMS, which was costly, and I don't know if they had made a compelling Android app (wikipedia says they did have an Android app; but who knows if it was good); I never ran iOS, so I don't know if their iPhone app was any good, but I never heard from friends with iPhones that they were using it, so I'm guessing not so great.