Large firms will simply attempt to register their names in all of these top-level domains. The other problem would be achieving consensus on appropriate shortened forms of the names and the appropriate granularity. There are 10 top level categories in the SIC codes with about 97 distinct categories at the two-digit level. What is important is that the Internet names map onto the SIC classifications in a reasonable way, not that the mapping be perfect. It also may make more sense to use UN industry classifications in order to encourage international acceptance.
Related problems arise in other aspects of managing the Internet.
Despite the fact that the Internet is highly decentralized, both respect to its technology and its management structure, there are some areas that could qualify as natural monopolies. Although this process can be decentralized to some degree, there should be some final authority for resolving problems. Such an authority would likely have to have some legal standing, which would presumably be backed by the courts. There are other issues, such as the Domain Name System mentioned above, where industry efforts at coordination that arise need to be legitimized by legislation. Such coordination roles may well involve some degree of monopoly power, though the amounts of money involved are often quite small.