Cardio is the sole reason I do indoor biking. I was very sick and couldn't do much, so I tried having mild biking effort as a way to rehabilitate my heart.

I used to do exactly what you suggest: bike + full workout. I liked it a lot, but it's not integrated as in a sport. It was odd for instance, I had much more "power" than ever, so much that I couldn't run anymore because my thighs were too strong and I had to relearn how to land my foot otherwise I'd miss the ground.