You're forgetting that CTV are not able to simply grab half an hour of airtime whenever they wish. They're tied in to the network's schedules. If CTV were to broadcast a local politics show at, say, 7.00 pm on a Thursday, they would deprive viewers of that evening's episode of Emmerdale. Without going into the relative values of individual programmes, some people would be highly put out by this - perhaps a great many. They would complain to CTV, ITV, even Ofcom and/or use their Sky boxes to access Emmerdale from another ITV franchise. Result - a lot of fuss and lost CTV viewers.
With a CTV Politics Programme, there's also the question of how it would deal with Guernsey issues. Whatever CTV transmits Guernsey gets. Guernsey folk would expect equal treatment for their States and issues, so you'd end up with a programme whose very existence, depriving them of their beloved soap-opera, would piss-off a lot of people and which, if it balanced Jersey and Guernsey, would be irrelevant to 50% of its viewers for half its time.