In my quite-less-educated-than-Stu-McGill opinion, I don't think it's doing yoga, or the quality of being mobile, or developing flexibility that is the antithesis of being and elastic athlete or powerlifter. I think it's that someone who primarily does yoga, acrobatics, dancing, and such is not someone who typically develops stiffness, because they don't train that way. Likewise for strength athletes - primarily, they are training tension, stiffness, muscle mass. But I've not seen proof that developing the opposite quality within the context of what one "is" would ruin one's strengths. If a flexible athlete trained to be able to have stiffness, I doubt there would be any harm to their primary abilities. Similarly, if a stiff athlete develops flexibility, I tend to doubt there's harm there either. But if either one switches their TRAINING to be PRIMARILY the opposite type of training, then they start to turn into something that is in between, and eventually (over years, or decades, in extreme cases) go towards the other side, and "lose" what they once had, while gaining the opposite. Whether or not that's desirable is a matter of choice.
I've never found a disadvantage to developing or maintaining flexibility. Exploring and practicing movement keeps us young. That said, I don't feel like I have to have it, either. Doing the type of training I want to do (currently Olympic Lifting) maintains the mobility for that type of training, though I do put in some extra work from time to time on shoulders, hips, ankles, t-spine. I can't do yoga as well as I could 10 years ago before I started strength training. (Well, technically, I can "do" yoga just as well... because it's more about breathing, the mind-body connection, focus, etc.. And that can be done no matter how well you can do the poses.) But I can't get into the poses as well. Also, I am 10 years older. So I think it's all 3 things -- 1) not practicing yoga as I used to, 2) being older, 3) developing more stiffness and muscle mass for strength and power, since that is how I primarily train these days.
On a final note, stretching is a wonderfully relaxing tool to have. It's available to anyone. I wouldn't want anyone to be afraid to stretch any more than I'd want someone to be afraid to do resistance training. Topics like this which may have lessons for elite athletes can sometimes put up unnecessary barriers for us mere mortals.
I've never found a disadvantage to developing or maintaining flexibility. Exploring and practicing movement keeps us young. That said, I don't feel like I have to have it, either. Doing the type of training I want to do (currently Olympic Lifting) maintains the mobility for that type of training, though I do put in some extra work from time to time on shoulders, hips, ankles, t-spine. I can't do yoga as well as I could 10 years ago before I started strength training. (Well, technically, I can "do" yoga just as well... because it's more about breathing, the mind-body connection, focus, etc.. And that can be done no matter how well you can do the poses.) But I can't get into the poses as well. Also, I am 10 years older. So I think it's all 3 things -- 1) not practicing yoga as I used to, 2) being older, 3) developing more stiffness and muscle mass for strength and power, since that is how I primarily train these days.
On a final note, stretching is a wonderfully relaxing tool to have. It's available to anyone. I wouldn't want anyone to be afraid to stretch any more than I'd want someone to be afraid to do resistance training. Topics like this which may have lessons for elite athletes can sometimes put up unnecessary barriers for us mere mortals.