They're just not anti-government enough for a lot of people; for example, their journalists don't get to tell readers that every single Covid death was caused by Boris and he should go to jail for criminal manslaughter, even though that's clearly something they back given... certain retweets.
Even Australia with only 25 million has two, and IMO it's nowhere near enough. Ireland has two.
Germany has twelve and through those also participates in two transnational public media organisation. Much of it is a purposeful legacy of the allied occupation because one of the earliest things Hitler did is consolidating all broadcasting.
Why you ask have more than one public media organisation? Because you ensure diversity of opinion, create a resilient network, create specialities, ensure regional representation, provide funding and funding options, provide diversity in all manners, more independence from government interventions, etc., etc.
Spain has 13.
The public service remit is vital.
And don't use the term 'broadcaster' for the concept because it limits their role. It might be much of what they do, but think video game funder, social media, keeper of historical heritage, open-source development, educational platform, trusted source of facts (as in Wikipedia), diplomatic tool, amplifier of diversity in all aspects, keeper of audio-visual libraries ... the possibilities are endless.
They are both editorially and operationally independent from the government (which is why this government hates both of them).