I'm sure the ugly buildings, connected to the beautiful old council buildings by an even uglier concrete corridor, will be sorely missed.
http://www.bbc.co.uk/news/uk-england-coventry-warwickshire-30827962

Remove the tunnel and those buildings have a lot of life left in them. Seems that people have money to burn.

But my real worry is that the City is becoming over reliant on the university. What happens if (when) it all goes belly up?

In some ways the university has saved some buildings from the demolitian men.The old Gaumont and part of the Gulson Hospital to name a couple..But-if they are selling to the university, what do they do with the money and the rates paid for them.
Or do they give them away? The buildings coming down have not been up all that long-so why waste money pulling them down.If the council house is vacated as forecast-what's the betting that the university will not get that too. It is heated-to save money??? by the free heat from the refuse disposal plant at Whitley, which cost a few millions to do only a few years ago.I remember the roads being up for months to install the gigantic pipes.
Coventry needs more meeting halls and what would be a better place than right in the centre.

Sadly it may go the way of the Whitefriars monastry--locked up and used for 'storage'.

Some good's coming out of this: http://www.coventrytelegraph.net/news/coventry-news/ugly-city-centre-bridge-demolished-12357717

Good riddance to that thing!

Yes, it is a particularly feature, especially being attached to the side of the Council House.