I agree with your logic 100%, except I would be very sure to not go crazy with the product tags either. IMO it's generally enough to mention the model number, product name, etc. in the question. The tags become more useful when there's a large body of Q&A related to a particular thing. When there's only a handful of Q&A about a particular product then there's really no need for the tag to be created just yet.
Also, most issues, though specific to a particular hardware/driver/software version, should be solved using the same basic blueprints. So hiding a general purpose solution under the guise that it's product/vendor specific is just causing us to write 10 different answers for the same general questions.
What do I mean by this?
Well if we have a question that's asking how to map some special keys on a Lenovo/Thinkpad keyboard, the same approach can be leveraged by anyone. The same tools will be used to determine the key's scancode, the same tools will be used to map the key to something else, etc. So we're doing ourselves a huge disservice by tagging these questions with vendor/product tags.