Before introduction of Power Meters, heart rate-based training was just about the only affordable data driven option for most athletes and it still is. Heart rate monitors are a commodity product now. Many people even wear one 24/7 in the form of a smartwatch like Fitbit or Apple Watch. Moreover, HRZ based training can cross-functional -- it can apply to cycling (indoor and outdoor), running (indoor and outdoor), rowing, and swimming and the concepts are the same across all sports.
That means, for example, that if you usually train on Peloton Bike, and some days you want to run instead, you can continue with HRZ-based training no matter what. It also means you can take rides in studio and at home and treat them as HRZ-based workouts.
Both are important. HRZ teaches you how to listen to your body and interpret heart rate graphs. HRZ concepts can also be applied to cross training, since your heart is always with you (hopefully) and HR monitors are ubiquotous and cheap these days.
FTP is a measure of your progress in PowerZone Training. HRZ-based training progress is measured differently.
As you train and your fitness improves, your heart becomes stronger and is able to pump more blood with each heart beat. Your resting heart rate gets lower, and your power output at a given heart rate increases -- your power/bpm ratio becomes the measure of progress.
An FTP test plays a role in establishing a baseline. In HRZ-based training the power/bpm ratio becomes more important than the absolute value of your FTP. That means that as you reach your physical limitations and your FTP flatlines, you can start focusing on other metrics.
Heart rate is highly dependant on your general well being and state of mind. The same workout you take today may have a different power/bpm ratio than on another day. Your heart rate is influenced by your emotional state, stress levels, sleep quality, and so on. What matters is a long-term trend.