No it is still flawed because other than people that openly admit to wanting a talking shop/protest party they wouldn't acknowledge that their ideas and potential policies are "unelectable".
In fact the socialist broad brush is often misused on here and some know they are deliberately doing it. You could say the same for "heartless tory bastards" but that's for another thread.
"1970s socialist" became something of a pet insult for one shouty poster when half a dozen people had him on ignore. It was easy for him to assume that people ignored because of a shared politics when in actual fact it was because of his behaviour and overly argumentative and critical analysis light style of posting. And plenty of the people he accused of being socialist weren't.
Your analysis is also based on the idea of a centre ground largely defined by the establishment, the powerful and media elite.
So the "centre ground" isn't actually the centre ground but to the right of it, although on social reform issues it may be to the left of it at times.
Whilst it is difficult to change people's ideas and outlook on life most of the general public are relatively poorly informed and don't critically analyse political information properly.
When people are told the government has run out of money and the last government left a note to saying sorry and it was meant seriously, unless they they are well informed or sceptical in nature, they are more likely to believe it than not.
It’s why emotional arguments and simple analogies and narratives are often the most effective at winning elections. People don't really want to hear that the real world is a complex place and it requires complex solutions.