Why the Same Injury Keeps Coming Back
The obvious move when something hurts is to treat the thing that hurts. Ice it, stretch it, rest it, strengthen it. It is logical, and it is why the same injury keeps coming back.
Pain shows up where the load lands. Where the load lands is downstream of wherever your body stopped organising force properly.
The hamstring that will not stay fixed
A pulled hamstring is the clearest example, because almost nobody who pulls one pulls it just once.
The hamstring does not work alone. It works with the glutes, the hips and the trunk to decelerate a leg travelling fast. When the glutes are not contributing, or the hip on that side is not stabilising, the hamstring is left absorbing force it was never meant to absorb by itself.
Treat the hamstring and you treat the tissue that failed. You have not touched the reason it was carrying that much in the first place. So it heals, you go back to sprinting, and the same hip sends the same load to the same muscle.
What has to change instead
The unit of work is the whole chain, not the sore part of it.
For a knee, that means the relationship between the glute medius and the VMO, because those two are what keep the knee tracking where it should when you cut. Strengthen that relationship and the knee stops absorbing rotation it was never built to absorb.
For a shoulder, it means the muscles that anchor the scapula, not the rotator cuff on its own.
The pattern is the same everywhere. Find what stopped doing its job, get it working again, then put load back through the whole thing and see whether it holds.
Why it is worth the longer route
It ends the cycle. An injury that keeps returning is a diagnosis that has not happened yet.
It also makes you better while it fixes you, because the thing that was missing was a real capability and now you have it. A hip that was not stabilising is a hip that was not contributing to a sprint either.
And you find the next one early. Once you are looking at how force moves through somebody rather than at where it hurts, the imbalance is visible before it turns into an injury.