Should a house be open to the public after the owner dies? Should it go to some government?
There isn't any sort of consistent logic here. Once you think about assets, companies, multiple people working on something etc, it will never make sense to think someone dying means all their work should be free unless they own it and make it free in their will.
The right to legally enforcable exclusivity in intellectual property regimes like copyright or patents stems from a balancing exercise between incentivising the work being done (i.e. authors writing books, filmmakers producing films, drug companies researching cool life-saving medical innovations etc.) and ensuring that at some point it reaches the public domain (plus a bit of practicality).
Human leisure, desire and opportunity to consume artistic works is a fair of the population size, and is not unlimited.
That's why you don't see a unique and profitable theatre company present on YouTube for every individual of the population.
Also there are already time limits for things to be in the public domain and medicine patents expire and become public domain, so I'm not sure what your point is.