Why don't governments design sites with multiple themes for multiple targets? And speaking of being accessible ... why do their sites have so much small text? No, I think government agencies could make better use of fonts and sizes, at least.
Really though, the chances that tertiary government - like the ones who manage a city - keep a website designer on staff seem low. What would he do the other 360 days of the year? If they want to buy something like that, chances are it has to go out to tender. IT departments in non-IT firms are likely to be predominant busy with dealing with network issues, making computers run far too slowly, and issuing new mice and keyboards.
Heck, their CMS is certainly government procurement service. They advertise the fact on their site:
The real question is why a bunch of councils don't stick their money together and lock a bunch of programmers up in a basement to make cool tools for them.... That would seem the obvious thing to do - what are the odds that your council has a demand that no other council has?
Would you want to be the person working for that organisation?
Working for one council means working for a committee, working for multiple is probably working for a committee of committees.
Decentralisation and out-sourcing are central words for the public society. The idea of bringing this in-house and sharing between other councils is probably a couple of pay-grades above the person on the comms team who is in charge of the website. The person in charge of the website may not even be a "technical" person and have time to think of all the cool possibilities.
MySociety make fixmystreet for councils (the open source fixmystreet.com but hooked into councils existing systems + extra reporting), I'm sure there are plenty of private companies making these things and selling them.