That was one of the ideas I am trying to get across in the Hillfit book - basic, simple strength training for hiking and backpacking.
This is another study that highlights the benefits of strength training for stroke survivors:
Maximal Strength Training Enhances Strength and Functional Performance in Chronic Stroke Survivors.
After training, leg press strength improved by 30.6 kg (75%) and 17.8 kg (86%); plantarflexion strength improved by 35.5 kg (89%) and 28.5 kg (223%) for the unaffected and affected limbs, respectively, significantly different from the control period (all P < 0.01). The 6-min walk test improved by 13.9 m (within training period; P = 0.01), and the Timed Up and Go test time improved by 0.6 secs (within training period; P < 0.05). There were no significant changes in walking economy, peak aerobic capacity, Four-Square Step Test, or health-related quality-of-life after training.While this study did not look say quality of life improved, the Get up and Go test and the walk distance certainly indicate improvements in function.
Maximal strength training improved muscle strength in the most affected as well as in the non affected leg and improved Timed-Up-And-Go time and 6-min walk distance but did not alter Four-Step Square Test time, aerobic status, or quality-of-life among chronic stroke survivors.
There is a similar study here (full pdf available) High-Intensity Resistance Training Improves Muscle Strength, Self-Reported Function, and Disability in Long-Term Stroke Survivors
Walking, getting out of a chair, climbing stairs...these are skills for which we need strength as we get older and as we get injured.