It's worth saying the BBC has been 'doomed' for as long as I can remember. Simply pointing out that it doesn't make sense doesn't seem to have much effect on its continued presence.
It's entirely possible that the BBC is maintained for another century, purely as an expensive monument to the country's history that nobody watches, before finally being rolled up in 2092. There's precedent for this in things like the royal family[0] or Brexit. Or tomorrow the Tories wind up repealing the license tax and significantly downsizing the BBC as a result, turning it into an English PBS/NPR. Knowing that the BBC is doomed doesn't tell you how long it has to live, just that things will continue to get worse until something breaks completely.
[0] Conflict-of-interest disclosure: I am an American
This is not truthful - the World Service is funded by the rest of the BBC, not the other way around, and until recently was also funded by the FCO.
Big budget costume drama your commercial broadcaster paid $$$ for? BBC Studios. Guy speaking your language but likely from a radio studio thousands of miles away, telling you stuff that your local news media are too scared (if they exist) to broadcast? BBC World Service.
Historically the UK government saw the BBC World Service as an important way to exercise soft power, and funded it directly. That ended, and today it's all paid for out of the profits of BBC Studios and the license fee.
"Licence fee accounted for 71% of BBC funding in 2019/20"
https://commonslibrary.parliament.uk/research-briefings/cbp-...
See for example All Largely Propaganda from "Bang!" - An Open Letter by The Hafler Trio.