The Birling family, plus Sheila's fiancée Gerald Croft, are indeed primarily concerned with appearance. Each of them when questioned by the inspector reveals that their cruel actions towards Eva Smith were driven by a need to protect their own reputations and to allow them to appear noble and upstanding citizens. Mr Birling sacked Eva for participating in a strike, which would have raised public awareness of Birling's low pay for workers. Sheila Birling was affronted by Eva's beauty which exceeded her own, so had her sacked from Milward's store. Gerald had an illicit affair with Eva despite being engaged to Sheila Birling - the more commendable social match. Eric was the father of Eva's unborn child and became a thief - stealing from his own family - to support her. Mrs Birling through her charity committee refused to help Eva as she felt the girl's situation was of her own making. The inspector reveals that each of the characters are responsible for Eva's death and that
if men will not learn that lesson, then they will be taught it in fire and blood and anguish.
The characters need the jolt at the end of the play to reinforce the message of the inspector. As an audience we do not know if the lesson is truly learnt.