Assertion of intellectual property rights over languages is happening. Here's an FAQ in a public archive for Australian Aboriginal material (ASEDA, AIATSIS).
Q: Why do speakers restrict access to material in their languages?
A: Many speakers of endangered languages consider that their language is their intellectual property, passed down to them from their ancestors. If it is made freely available to others, then their rights in that language can be diminished. Usually they do not want strangers to use words and sentences of their languages in an inappropriate way, and want to be consulted prior to public use.
At Language Log, Mark Liberman has a couple of comments on Tom's recent post about this with respect to the Mapuche people's complaint against Microsoft, and following Geoffrey Pullum's post on the same topic.
If this idea were really to be accepted into the system governing the usual laws of property, I suspect that the consequences would surprise and displease many of those who start out supporting it . For some discussion, see "The Algonquian morpheme auction" (3/3/2004).
To the bad consequences... The "usual laws of property" is the soft spot. What are they? We're dealing here with people who by and large have customary ways of behaving, sometimes called customary law, rather than written statutes. Bringing customary law into a legal system is tricky (cf. the Australian Government report The Recognition of Aboriginal Customary Laws)—but possible.
Take the example of land held in common by Indigenous people. In Australia, recognising Aboriginal title to land required passing an Act (Aboriginal Land Rights (Northern Territory) Act 1976) which allowed Aboriginal Land Trusts to "hold title to land in the Northern Territory for the benefit of Aboriginals entitled by Aboriginal tradition to the use or occupation of the land concerned". This in effect created a special land title, Aboriginal freehold title, one which is owned in common by the members of the Aboriginal Land Trust. The land held by the trust cannot legally be bought or sold.
A similar process could be developed to look after property rights held in common for languages. So the bad consequence mentioned in "The Algonquian morpheme auction" — Disney owns my language! — could be blocked. But the costs would be huge, both in developing the process, and then later, since bringing customary law into the seductive embrace of the state will probably just fatten the litigious and their helpers (as noted in an earlier Language Log post).
Mark Liberman then asks:
Here's a question: if the use of a language has to be licensed by the tribal elders, can they withhold this permission from someone who wants to criticize them, or to say something else that they don't approve of?
I'm guessing he's thinking of a group withholding permission from an outsider to use their language to criticise them. In the Australian Indigenous societies I know, people have the unquestioned right to speak the languages accepted as their parents' languages. So "tribal elders" aren't on about licensing kids to speak their own language. But outsiders? Well, I can't see why Indigenous communities couldn't have that right. Just as copyright laws allow a map-maker or a publisher to refuse a critic permission to republish a map. Or trespass laws allow me to prevent a critic from coming onto my land, let alone erecting a billboard on it criticising me (however justifiably).
Three differences are important here - a difference between rights held by an individual and rights held by a group, a difference over which rights can be traded and which are inalienable, and a difference as to whether a right-holder has the right to license other people to enjoy some part of that right. Individuals—so Australians, North Americans and some other groups believe—have rights to control access to land and re-publication, and to buy and sell those rights, or licences to them. We allow people to assert rights to some words as trademarks, and to license others to use the trademarked words. As for groups, leaving aside companies and trusts which act as pseudo-individuals, we (well, most of us) think it reasonable for groups—our governments—to assert a basic right to control access to our countries (sovereignty), and we're pretty wary about selling off this right.
Some Indigenous groups don't recognise individual rights to trade in land, or to trademark words, or to sing another person's song. They do assert rights as a group to control access to their land and to their languages, but probably not to trade those rights. Sovereignty over languages as well as land. But in actual practice, probably the best way of getting rights over language recognised (unless money is involved, as it can be) is to rely on what customary law relies on - politeness, and educating outsiders as to what is polite. Which is the flipside of Mark Liberman's comment "Whatever the outcome, linguists' best protection against such problems is to be solidly based in the speech communities in question".