The authors recognize that. The problem is that line extended products don't connect to the things you have associated yourself with in the customer's mind. If Dial makes body wash...line extension is probably acceptable. If Dial makes toothpaste, deodorant, or snack food the connection of Dial <=> soap isn't there as strongly.
They make the point that in long run you're diluting your brand. You can only occupy one particular place in someone's mind with a single brand. Owning that position is valuable. Owning 'they do everything' is not really a winner. That feels like 'they do nothing well.'
Yep. There are plenty of counter-examples of companies that set up different brand names that become stronger than a shared brand could ever be. For example, Unilever has many strong brand names: http://unilever.com/brands/?WT.GNAV=Our_brands
Large breweries often have many different brands that are perceived differently by people.
It's hard to build a strong brand name, but if you can pull it off and avoid line extension, it's the better way.
They make the point that in long run you're diluting your brand. You can only occupy one particular place in someone's mind with a single brand. Owning that position is valuable. Owning 'they do everything' is not really a winner. That feels like 'they do nothing well.'