Hardly. When my office moved from 3 to 10 miles from my home and I was just riding around ( 4000-5000 miles a year) I was slower commuting than the last century I rode because once you have a little fitness (perhaps a thousand base miles) riding more doesn't make you significantly faster.

A training plan with heart rate made a big difference. Power made it simpler to ride as hard as practical on hard days and boringly slow on rest days for bigger gains.

If you want to ride to be faster, go farther, or loose weight and are putting a reasonable (six hours a week?) amount of time into cycling you want a structured training plan although you don't need to be too parochial about it (sometimes substitute a sweet spot ride with friends for your 2x20 day, fit intervals between conveniently spaced traffic lights as opposed to trying for exactly 300 seconds of interval with 300 seconds of rest, whatever).

If you're not yet doing that experimenting with heart rate would be less expensive than training with power.