I need to get out more often. Thanks to the relevance search, I have not used All Contacts view since the awkwardly named Dynamics 365 July 2017 Update seen the light of the day. Because if I have had, I would have noticed that clicking on any contact in this view opens New form instead of opening the existing record. Demian “Sostenga mi cerveza” Raschkovan pointed that out to me and casually mentioned that copying the view and replacing the system one with the cloned copy solves the issue.
Credit is where credit due. Nishant Rana mentioned this bug in October last year. And I like the workaround by Davide (thank you – whoever you are!) – just add and remove any column, publish customizations and the system view is now working!