If a musician doesn’t have the right to their own work, it’s because someone offered to pay them for the rights and they accepted.
Is that in their favor? I think so, considering the alternative is to not get paid and not have rights to their work.
And not to go too far off topic, but publicly funded research is generally not aimed at drug development, it is aimed at discovering the basic science behind how the body works (human body or otherwise).
If you want a clinical trial that proves a particular drug can actually help patients, you will need to find a company to pay for it. The government almost never pays for clinical trials (I think the COVID vaccine might have been an exception). Clinical trials are far more expensive than basic science, and patents are the carrot to get the private sector to pay for them.