There are a few things the model doesn't capture. Namely:
We develop a model in which the benefit of language acquisition is increasing in the number of individuals who speak the language. This gives rise to a network externality, and if language acquisition is costly, the language acquisition decisions by individuals may be inefficient. If the available policy instruments affect all members of a language group homogeneously, then policies that effectively subsidize language acquisition are warranted only for the majority language.
1. Some argue that learning multiple languages may have positive cognitive benefits in young children. I haven't found much credible evidence of these effects. Also, this is irrelevant in the U.S. since we teach teens languages, not kids.
2. Some think that learning languages (mostly just Spanish) will make people more culture and less racist. I don't know what to make of that. Why not just teach culture and the philosophy of tolerance? And most "cultured" people are bigots (see: Cambridge, MA).
3. This model applies to one country. Maybe someone could think of a reason international integration is only possible by unifying under like 5 languages, common to everyone. The model, at a world level, suggest that would be a wasteful strategy. But perhaps there are gains the make up for those costs from integration. (Europe seems to be doing fine with just English, though. And in the short run this seems irrelevant.)
Also, these results are for general equilibrium for teaching large numbers of people. Of course people who plan to move to Japan should learn Japanese. And Mexicans who plan to move to the U.S. should learn English (wait.... maybe that isn't so obvious?). Individuals can still gain from learning languages, but society as a whole will lose if lots of people do this. Gains to individuals are more than cancels by losses they cause for other people.