Take a look at this revision for an example: https://webapps.stackexchange.com/posts/50481/revisions
I don't see a reason to remove the more general tags. They make it much easier to find an answer and provide better visibility. Personally I do not follow as specific tags for everything, so I miss some Google related questions that I may be able to answer simply because their less specific tags are being removed.
Superuser Meta had a similar question and it would appear that less specific tags shouldn't be removed.
Take a look at the tags I have favourited. I would miss a question like mine above asking a Google Presentation question, however I would most likely be able to answer it.