Show the education to whom? We show it to people every single day. All home educators do, every single time they interact beyond the nuclear family, and they/we DO celebrate. We DO show off, we ARE proud, and we express that pride and that joy to the people who support us (families, friends, local community) and the people who can offer us practical help and advice (other home educators, local, national and international).
Why would we want to be proud and show off to a Local Authority employee? I just don't get it. (S)he has no practical help to offer (no budget for home educators), and is very unlikely to have as much knowledge of what opportunities there are locally and nationally as the HE groups we are all networked with nowadays. On the other hand, (s)he DOES have the power, on a whim, if we let him/her into our home, to say "no, I don't think this education is suitable". And then we find ourselves in court arguing against a school attendance order not on the basis of concrete evidence but on the "expert testimony" of someone who we let into our homes intending to celebrate, show off and be proud of our educational provision with.
It's a power imbalance - can you see that, and appreciate how dangerous that is for the people (HEers) with less power in the scenario? Even if 80% of LA employees were kindly disposed towards home education, think about the severity of the consequences if the person visiting my house is one of the other 20%. That's the 20% who thinks that school is ideal for almost every child, who thinks that autonomous home education is lunacy, who thinks that children with invisible disabilities just need stronger discipline. It just isn't worth the risk. Do you see that?