Billing for Time Is One of the Colossal Stupid of all Money Making and Money Spending Approaches to Business

I have been thinking about hourly billing – billing for one's time. This has to be one of the colossal stupid of all money making and money spending approaches to business, a holdover to sweatshops and day labor.
The problem is time is the least and most valuable thing I offer and have. I can't make any more of it and it doesn't equate to my level of contribution. How can I possibly put a value on my time?
Billing for time misses the entire point of my work and worth. No one wants my time. They want the results of my work.
And the results of my work are worth spending something on. The same applies to countless consultants, coaches, and advisors across the globe.
The point I want to make is this – the time of a professional is the least valuable thing they have to offer. And professionals that tout a high hourly rate are playing games to benefit their ego. You can't put a rate on your time.
But you can put a rate on your value and the benefits you deliver.
What do you think? Do you like billing for you time or paying for some else's?