Public "demand", which in truth I don't think is there anyway, beyond the vested interests, has little relevance against the legal implications of doing so. That's really all that matters. Whatever the outcome, those who howl at the moon about City being cheats are going to carry on doing so, it's not dependant on whether UEFA take action or not. Football clubs aren't like normal commercial entities who seek customers and can't cope with negative publicity, it doesn't work the same way, and it certainly doesn't work the same way with those who oppose them. Now, if City really were guilty of cheating systematically, then absolutely it would have an impact over a longer term, but I don't think many who are disinterested would think that is the case - and lots of them consider the whole FFP concept to be infinitely worse, and a specific attempt to protect a cartel.
Some people shout very loudly. That's normal enough, but outside of the social media/media circle, I don't see hostility to City, I see indifference, and wry amusement at the attempt to stitch up football.