You might value your time more than your money but how will you feed yourself if you don't have it? How will you buy your daily necessities without it? The real reason why everybody use fiat currency is because of it being used by most of the people alive on Earth.

I might not be able to convince you but the usage of money in our society is important because it helps the economy of every country grow. Without a medium of exchange(for work done), then everyone wouldn't work and it would be chaotic. You might say that we can use goods to pay for jobs, but isn't it easier to exchange using fiat currency($)? Also, if people started to create their own time, who would supply the pay?
It is not easy but it is possible but the pay for each job will still depend on how much the one who hire pays for it unless there would be a general consensus in minimum wage for each job.