I think you need to extract your head from your metropolitan bottom, dear boy.
Parliament is hardly comparable, Westminster Hall is almost 1,000 years old which does set TVC's magnificent half-century in a bit of context. Though in point of fact, Westminster Hall is no longer used for the principal business of Parliament and many MPs and committee meetings don't even use the 'newer' (19th century) parts of the Palace of Westminster, making use of the new building over the road, Portcullis House. So even our most venerable institutions, those with properly old buildings, aren't averse to moving on to something newer and more fit for purpose when appropriate.
TVC is a very specific building in terms of its design purpose. It was made to facilitate TV production as it was understood when TV production was a new art form. Things have changed in ways that those pioneers could not have imagined. It may not be the nostalgic option, but abandoning TVC is certainly the correct option for a publicly funded body with an obligation to make best use of its resources.
And on that point, the move to Salford and the expansion of BBC facilities all over the UK is likewise exactly the right approach for a body that collects money from the public. Where the BBC spends those funds is of great importance; every since its inception it has been drawing money from parts of the UK economy that can ill afford it and splurging it about in one of the wealthiest cities on Earth. The UK is in both administrative and cultural terms a highly centralised place and it requires a major effort by an organisation like the BBC, which reaches into both spheres, to help redress the balance.
London to Manchester is not far at all, neither by train or by air and, eventually, HS2 will close the gap still further. The only real gap is in the minds of the metropolitan numpties who think riding a tube train to its terminus is a grand adventure.
You know, this reminds me of when I lived dahn sahth, and watched BBC London run a news report moaning at how two London clubs' fans had to travel UP NORTH, USING THE M1 *AND* THE M6 to Old Trafford for an FA Cup semi final early one Saturday morning. All this was done with a completely straight face and not a trace of irony nor any acknowledgement that northern teams' fans have been getting up early for trips to the grotty London suburb that hosts our national stadium for decades without complaint.