I've been riding for three years now and still consider myself a noob. I have power on my indoor trainer but not on my outdoor bikes (8 total).
Cost is the only reason that I don't yet have power outdoors. Were I Elon Musk, I wouldn't bat an eye at putting power on all of my bikes. In fact, I'd have my personal assistant tend to that this morning.
Interval training is a powerful tool for getting stronger. And I find defined interval training easier to do with power data than without.
On rides that are not part of my regular routine, I find that power allows me to pace my efforts more carefully.(Zwift so far). I can do the same with heart rate but heart rate is a lagging indicator and, therefore, is less easily manipulated in real time .
My favourite thing about power data is that it motivates me by providing me a way to objectively measure small increments of progress. Combined with a heart rate monitor, I can work out my efficiency in heart beats per joule output and see that improving over time if my training regimen is effective. After my first year of riding, my rate of progress slowed so much that it became nearly imperceptible on a month to month basis without the power data.
I recently found out that Trainer Road has a machine learning algorithm that estimates the TSS for a ride based on heart rate data alone. Assuming that it works, I'm excited about that as it will somewhat obviate the "need" for me to have power data on my outdoor rides