What an ill-conceived idea!
The decision to be FTA or not and the further decision to cough up for EPG fees is a Commercial one for each and every Broadcaster.
Nothing whatsoever to do with Government.
The "logic" in the grounds for the Petition is disjointed, factually incorrect and specious.
And, inevitably, the Petitioner perpetuates the disingenuous error of equating the UK TV Licence to funding of the BBC. The funds may indeed find their way there, but read the Licence: It gives you permission to operate equipment for receiving TV transmissions - any TV transmissions.
If people think a specific Channel (or group of Channels) should be free, then lobby the provider of that Channel. But they are businesses, not charities and I imagine they know better how their own business model works than a few ill-informed potential viewers.