Not mixing it up can lead to burning out or overuse injuries such as tendon injuries, muscle strains, or even stress fractures.
The American College of Sports Medicine recommends incorporating cardio respiratory, resistance, flexibility, and neuromotor exercises, sometimes referred to as functional fitness training, into your regular routine. Incorporating just one other activity into your training regimen isn’t going to cut it, but doing multiple activities that include aerobic exercise, strength training, stretching, as well as balance and coordination training will provide the overall health benefits we all need . There is even evidence to suggest that adding exercises focused on improving core strength can help to prevent injury particularly in the hips and knees.

Yoga falls under functional training
Cross-training can be a valuable aspect of a fitness routine once injured. If the appropriate activity is selected an individual may be able to continue to improve cardio respiratory and strength without causing further injury.

It’s all about proportions
References:
http://www.acsm.org/about-acsm/media-room/news-releases/2011/08/01/acsm-issues-new-recommendations-on-quantity-and-quality-of-exercise
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3806175/pdf/10.1177_1941738113481200.pdf