A couple reasons. First, an exercise/activity routine isn't really well-rounded unless it includes multiple facets: strength, stamina, balance, agility, flexibility, and more. Second, flexibility or lack thereof is associated with other health conditions. For instance, having tight hamstrings (which I do) is associated with lower back problems. Thirdly, probably most important for me, I've been prescribed specific stretches to deal with repetitive strain issues in my shoulder and hip, and stretching - when I'm consistent - really is helpful.
Re: stretching