J
My guess is that anyone who has valid reason to be concerned about identification for security purposes also has the ability to register an aircraft through a trustee or limited company with a nominee account. In fact quite surprised that given such concern you were not advised to do this by those who have created your need to remain secure (or your advisors).
Is it sensible or not?. On balance I think I would prefer not to have my name and address on a public database but I also recognise that anyone who really wants to find my address will do so through a number of different means including Google and other serach engines so I find it difficult to get too hot and bothered about the CAA placing my address on their database.
It does mean that members of the public who don't like me flying over their house might just pay me a visit and persuade me not to do it again but If anyone raneg my local flying club they would no doubt be told who the pilot was anyway and a few questions in the village would soon track me down.