When I first quit training karate, in 1994, a big reason was persistent pain in my hips, on the outside edge. It fell right into the range of not-debilitating-enough-to-keep-me-from-doing-normal-life stuff but painful-enough-to-interfere-with-training. I actually went to a sports medicine clinic to get checked out, but their help got me exactly nowhere.
A decade of inactivity calmed down the pain, but I have to admit I was kind of nervous about getting back into training - would the injury recur, would I be able to continue, would I be limited in my kicking, etc.
Luckily, one of the first resources I tapped into for information when I got back into training was Thomas Kurz. One fundamental practice of his flexibility routine is strengthening the hip adductors (your groin muscles - the muscles that pull your legs towards each other) in order to improve their flexibility (muscles that are weak in a particular position will tighten up, so if your adductors are weak while lengthened they'll tighten, while if they're strong in that position they won't, and you'll have greater range of motion).
I was doing Kurz's exercises in order to be able to kick higher, but a side effect was that my hips felt better than they had in years. Over the past five years I've made very gradual increases in my own range of motion (I tend to get lazy about the workouts, and I took another year off recently) and I'm not sure I'll ever do a full split, but my kicks are higher than they ever were before and my hip pain hasn't even flickered back.
What's the connection? I can't prove anything, but think about your hip for a minute. It's a ball and socket joint. The head of your femur fits into your hip like a baseball bat fitting into a cup. The socket is lined with cartilage - if it was all bone, then moving would involve two bones rubbing against one another, and that's not comfortable for anybody.
Now what happens to that ball and socket joint when you have muscles pulling on those bones? Imagine someone with very strong abductors (the muscles that pull your legs apart, on the outside of your hip) and very weak adductors (which describes me 20 years ago). Now think of your femur. It's going to have a very strong force pulling it to the outside of the hip socket - away from your groin - and a relatively weak force pulling it back in towards the midline of your body.
What's going to happen? Your femur is going to be pinched against the outside of the hip socket and grind against the soft tissue there. Think that's comfortable? Think again. What's going to happen to that cartilage and stuff over the long term, with that bone jammed up against the outside edge of the socket all the time?
Luckily, the solution is fairly simple - strengthen your adductors. The straddle to stand will work, although there are plenty of other options (sumo deadlifts, for example). Strong adductors will make your footwork quicker, give you better dynamic flexibility (which means higher kicks), all while situating your femur correctly in your hip socket so you don't get hip pain. Add direct adductor work to your routine about twice a week and you'll see some rapid improvements. I'm currently doing 3-4 sets of 3-5 reps of straddle to stands on Valslides, once or twice a week.
Where else do we see similar situations? Anywhere we have a ball and socket joint. How about the shoulder?
There are important differences between the shoulder and the hip - namely a much shallower socket. But to keep either one healthy balanced strength development is fundamental. To keep our shoulders healthy we have to pay special attention to balancing our strength across the joint - just the way we have to balance our adductor and abductor strength to keep our hips healthy.
With the shoulder, the muscles that push forward (pecs, front delts) and up (traps) tend to be very strong in karateka, while the muscles that pull down (lats) and back (rhomboids, lower traps, lats) are relatively weak. Basically, we spend a lot more training time pushing (punching, pushups) than pulling.
If you want your shoulders to stay pain free you have to balance all that pushing strength with a ton of pulling. Do chinups or pullups, rows (you can start with dumbell or barbell rows and work up to rowing yourself from straps you hang from your chinup bar). A nice little exercise I like is a dip hold - with your arms down at your sides, grab two handles - maybe the arms of a sturdy chair - and lift your feet off the ground. It looks like you've just finished doing a dip, but instead of going down and coming back up you just hold yourself in place, supporting your body with your arms. This trains all the muscles that hold the shoulders down in their sockets. Make sure you keep your shoulders packed while doing this!
Balancing the muscles in your body will not only improve your physique, it will improve your performance, make you more durable, and keep you in the dojo and out of the hospital.
So add in some adductor work, pullups, and rows to your strength training routine - don't ignore those movements just because they don't directly make you hit harder!