There are good reasons for muscle strengthening after stroke, of course. But therapists know these reasons well. For instance, the muscles on the affected side, even the ones that are the most spastic and seem overwhelmingly strong, are usually no more than half as strong as the unaffected side. Because spasticity is such an issue after stroke, some clinicians believe that strengthening "tight" spastic muscles will exacerbate spasticity. Research has shown that this is untrue; exercising muscles does not increase spasticity. It is important to focus on the muscles that are the weakest, of course. For instance, most stroke survivors have no problem at all bending their elbow, but extending their elbow is often very difficult, especially at the end of the range of motion. In this case it would be wise to work the triceps because it is the weaker of the two muscle groups.
The other form of exercise that therapists focus on is cardiovascular. Unfortunately stroke survivors get a double whammy: They are in half as good cardiovascular shape as age-matched couch potatoes, but everything they do takes twice as much energy. A good example is walking. Before stroke, walking takes very little energy. Most of the energy is expended in small bursts of muscle power, perfectly timed to use momentum forces and gravitational pull. After stroke, gait loses its subtlety and coordination. The gait that is typically left in the wake of stroke uses twice as much energy as prior to the stroke.
So cardio and muscular strengthening are important, but viewed as more of a "pre-process" than the process itself. In fact, many of the leading-edge treatment options (i.e., repetitive practice, CIT, forced use) are considered "intensive." They require that the survivor "hits the ground running" and be able to withstand the rigors of the intensity right from the get-go. In this regard there is a necessity for the survivor to be in pretty good cardiovascular and muscular shape prior to the initiation of treatment. Once the survivor has the stamina, the focus comes off the body and shifts to the brain.