The UK technically still is a monarchy, complete with a King, though they're more symbolic than anything these days. Allegedly.
Agree that the BBC is a hoary old monolith incapable of adapting or evolving in any meaningful way, & the very idea that it could be considered even a little "left-wing" is bewildering to me, but it's hard to get into that without being more political than is probably allowable or wise. Suffice it to say it does exactly what its told, even if that is to its own detriment.
The more I mull it over, the less sure I am making a deal with any streaming service is a good idea. Given how, for want of a better word, fickle those services can be - witness how often shows continue to be abruptly cancelled, leading so many viewers to question getting into a series in the first place - and how their business models seem less than sustainable, I doubt any of them could be a viable long-term partner.
Lastly, why would we assume that any and all issues, real or perceived, with DW are mostly or entirely because of Davies? External factors are clearly having a pronounced effect, as they have for a fair while now, and if there aren't executives at Bad Wolf, or far more likely the BBC, meddling, I'd be very surprised indeed. The age-old conflict between creative interests and commercial ones.