I think that’s a false dichotomy. Most of these old companies are addressing basic human activities, not problems. Unless you thinking eating good food and staying in hotels are problems that ought to be solved?
Most entertainment business are also not solving problems, and yet manage to be extremely successful businesses. See: Disney, Pokémon, video game companies, etc.
Yes, you’re right. (There’s also the “oldest profession”.) But I’d still like to think that many of these actually are problems to be solved, rather than unalterable facts of life. Look what happened to, for instance, secretaries. Or “computers” – i.e. the profession. Regarding entertainment, I don’t see how companies providing entertainment is an absolute necessity; people can be entertained by each other’s company, and have been for most of history and pre-history. Furthermore, the examples you give all rely heavily on copyright for their business models, a purely legal concept without a guaranteed future. If I had to bet on any entertainment company to survive for 1000 years, I would pick one which does things which can not be copied, like live performances, perhaps at specific historically important locations.
”Problems to be solved” is a narrow view of the mechanism of providing goods and services.
Is food a problem? Clothes? Housing? Historically societies that have lacked markets in these (grow your own food, make your own clothes etc) are not something I would call as aspirational models for our current civilization.
Most entertainment business are also not solving problems, and yet manage to be extremely successful businesses. See: Disney, Pokémon, video game companies, etc.