I've had issues with tennis elbow for pretty much a year now. I didn't rest at all in the beginning and simply toned down the intensity of my exercise. But gradually it became worse, until I had no choice but to take a break. First just a week, but it came back a couple weeks later, then two weeks, then a month and so on. Now I took an extended break of a couple of months. While resting might not be the answer (and I agree very often rest is the opposite of what you need), exercise certainly isn't always the answer either. If things were as easy as you think, everyone would already share your opinion.

Unfortunately I also have a very bad knee (osteoarthritis) and on some days I cannot walk from one room to the next without clutching every solid piece of furniture around me. Just recently, after years, I learned that it was movement that helped me most in such states. Of course I can barely walk and walking makes it noticably worse, but biking actually helps me quite a bit and rapidly improves my mobility and general well-being. But you kind of have to have the insight that moving is what you need, when you can barely move at all - and only certain kinds of movements too!

These issues are as complicated as anything else. Sometimes rest is necessary and sometimes certain movements are most beneficial. It's difficult to know. And rest is not a bad default, because while it might not help you, it rarely hurts you much worse. Training the wrong muscle when it shouldn't be trained can do some damage you might regret dearly for a long time.