1. Strong/flexible enough to excel at sport(s): Push-off on the run, power on the pedal down-stroke, and pull on the swim. Stride length, lower-back reach in the aero-position, streamlined horizontal posture in the pool. These are just a few examples of things that make an enormous difference in your performance that cannot be achieved solely by sport-specific endurance training. As a matter of fact, sport-specific endurance training often works against these aspects of solid performance, as your body tends to default to "what is most normal/comfortable" and hard-wiring current muscle memory, even though it likely isn't optimal. Rather, a much more efficient and accurate way to target the muscles and joints needed for sport is through functional-strength training. Since this is not an area of my expertise, I will not recommend specific exercises, but will say, this generally does not mean power-lifting and heavy weights, but rather, very controlled and refined movements that often use one's own body weight for resistance. The best exercises bake in strength, flexibility, and balance. If you read on and commit to getting serious about functional strength training, purplepatch has some great resources, such as their functional strength for runner's program (click and scroll down).
2. Without becoming injured: Being able to complete high volume sport-specific training requires incredible structural (muscular-skeletal) support. Think of strength and flexibility as an enabler to your high-volume training; lay the foundation by building good functional strength, and your body will better tolerate and adapt to the endurance training. The most simple reason for this is that toward the end of long days, weeks, monthly cycles, when you are most prone to lose proper form, you won't. Losing proper form means muscle imbalance and compensation patterns, which are probably the largest culprit of injuries in our sport(s). There is research showing that even some bone injuries (e.g., stress fractures) result just as much from torque on the bone (e.g., tight muscles, ligaments pulling the bone at attachments points) as they do from sheer impact.
Earlier I said this is one of the hardest things to actually do...and I will just tell it like it is. Most endurance athletes always default to using that last 15 minutes to get in another few miles or lengths of the pool. Stop. The marginal benefit from using that time to stretch or perform functional strength exercises is literally 10x more than those last few miles. This *does not* mean start cutting your workouts short. It does mean designing a training program that includes and makes the time for this, and if that means shortening some of your workouts, then so be it.
I'll end my post with a great quote from a yoga teacher. "Strength without flexibility leads to rigidity, and flexibility without strength leads to instability." For endurance athletes, I will add one last part..."and having neither leads to total meltdown and injury."
For more detail on functional strength (and all the pillars of performance for that matter) check out the purplepatch knowledge+ page. For runners, check out the purplepatch running plans.
Like I said before, there are other options out there, but I have started working with purplepatch because I truly believe in the approach and philosophy, and have seen how well it works first-hand, and in some of the athletes that I work with.