You'd think so, but the BBC found similar problems when launching their streaming services.

Annoyingly I can't find the link, but IIRC the BBC originally looked into making everything it had ever made in its giant archives available to stream. Even for the content the BBC produced and owned internally, which is a huge amount, they determined it simply wasn't possible to offer the full BBC back catalog all the time on their service - tracking down the various rights holders, actors, and other parties to the content to renegotiate for streaming was an impossible undertaking. A real shame - a readily accessible public database of all of the BBC's content would have been incredible, especially when so much of it was paid for by UK tax payers.

The last Labour government in 2010 was looking at options to legislate to absolve the BBC of these responsiblities, but sadly it didn't go anywhere. This is absolutely a problem that will need legal changes to fix for old content, realistically.

The simplest fix might be a mandated license for streaming old content where the royalties go to a collection agency and can be claimed by the rightsholders when they finally show up.

Maybe limit the collection time as well, so e.g. Any funds that have been sitting without a valid claim for more than a year go back to the BBC.

Except there might be a lot of rightsholders in the different territories. Figuring out how to disperse the revenue could be very difficult.

It is a weird idea to steal art from people and force them to sell it to others.

Compulsory licenses have precedent in the music industry.