AO is rarely painted. It is likely baked from a high poly mesh to a low poly mesh. Although there's nothing wrong with doing some hand-painting on top of the bake. It is used as part of a workflow that tries to represent mesh details using texture details instead, because vertices are expensive and texture lookups aren't.
For an example use case of AO, consider a game engine with a baked normal map. Because the normal map is not real geometry, but only tricks that manipulate the way that light bounces off the surface, a recessed area may get lighted in an inappropriate way-- after all, there is no genuine recess there, it's just flat geometry. If you wanted, you could just darken the diffuse texture in those recesses, but there is some lighting that should reach the recess. So you can use ambient occlusion to limit only the ambient lighting, without affecting other lighting.
This is all a trick. There is nothing remotely physical accurate about ambient occlusion, because there is nothing remotely physically accurate about the concept of ambient lighting to begin with. It is not a good idea from the standpoint of realistic lighting. It is a good idea from the standpoint of balancing a good looking picture with reasonable performance-- usually, the real-time performance demanded by games. Achieving this reasonable performance means that you can't use enough vertices to acquire the shadows realistically.
Some people recommend multiplying AO into diffuse for use in Cycles. This is not a good idea. If any texture artist thought that their diffuse should be multiplied by their AO, they'd just do that themselves in PS and skip the AO. Frankly, there's no real way to use AO in Cycles, because Cycles isn't designed for the same goals that game models and textures are designed. If you wanted to use ambient occlusion in Cycles, the closest you could get would be to composite (add) two renders, each using some subset of your lighting/world, and to multiply AO into diffuse in only one of those renders. That would leave AO occluding only some of your lighting, rather than all of it, which is the goal of the use of AO in game engines. So, no, in Cycles, if you use AO as properly as you can, it will not just get darker-- it will get darker in a specific way.
However, AO is appropriate to use in Eevee. Unfortunately, the only shader with an AO input is the Specular shader. Getting game-like renders out of Eevee, using AO, with other shaders, is again possible-- but only with compositing. In this case, a render without your world should use straight diffuse, while a render with your world but without your lights should use diffuse*AO. Your world is the ambient lighting in Eevee that should be occluded by AO. Again, if you use AO properly in Eevee, it will not just make your model darker, it will make your model darker in a specific way.