People will use Alexa to ask these questions with or without the NHS's publicly-available information. Except if they didn't use the NHS's publicly-available information, Alexa would use some other service like WebMD. The NHS' involvement (or lack of) would change nothing.

By your logic, Google is bypassing medical privacy laws because people can search 'what are chickenpox symptoms?' on Google Search.

Making information about medicines, diseases, conditions and symptoms freely available from a trusted source is a GOOD thing for society.