The concrete carbuncle was yet another reminder of how vast the TVC site really was. Not only did it already occupy a large footprint someone, at some point (I'd guess the sixties), thought that the BBC required even more office space... and put up a whole tower block.
I guess TV was a far more labour intensive business back then (for example, when I joined in 2000 the prospect of doing your own editing - without a craft professional - was seen as a non-starter by most staff in my department necessitating a trip to an in-house, or Soho, edit suite... now I imagine close to 100% would be quite happy to sit at a desktop machine and cut their own material) and the BBC did a lot more in-house but the BBC property portfolio was vast.
Not only did BBC TV occupy TVC... it also sprawled outwards to occupy other West London sites like The Television Theatre, Lime Grove, Union House, Threshold House, Centre House, sites in Acton and Ealing (OB's, VFX, Finance, Costumes and Wigs) and - latterly - the White City Building. Plus the whole Elstree Centre. All to house two TV channels that weren't even on-air 24-hours a day.
In fairness, that portfolio did slim down considerably over time as buildings were closed and formally in-house divisions were sold off or run-down (the results of John Birt's Producers Choice internal market) and - presumably - production and resources were allocated more efficiently, allowing programmes (WOGAN!) that were in other studios to be pulled into TVC (or just cancelled).
I never worked in the East Tower and - until the very end - barely visited it in all the time I worked there. It mostly (entirely?) housed the Children's Department and I never worked in that area. They did - of course - decamp to Salford leaving the Tower surplus to requirements.
I know the Tower was in quite a poor state of repair - the result of sub-standard construction - and I wouldn't mind betting that it was a headache the BBC would rather be shot off rather than try and continue to patch it up - or demolish it in the middle of a working office and studio complex.