The short answer is yes, wool is more expensive. It also is harder to work with than most synthetics in my amateur experience.
It is harder to source if you care about getting the knit/weave just so. Critters eat it. It felts unless chemically treated. It shrinks. You can't easily print giant logos on it.
It is worth it, though. And washing wool on the gentle cycle in cold water is just fine, as long as the garment can be reblocked and didn't require a lot of hand fitting work (good hand-tailored suits will likely require reconstruction if washed vs an engineered fit suit).
Cheers,
Will
William M deRosset
Fort Collins CO USA
I forgot to add: that said, I ran to work this morning in a wool t-shirt, socks, and underwear. My work togs all week include hard-finish wool overshirts and wool slacks, which get washed maybe three times a year.
And the wash fills up with the odd cotton bits long before the wool knits pick themselves up and wander off of the "worn, but not yet dirty" pile to the wash basket.
Synthetics last effectively forever, and smell of, well, me, after a few hours's use. Even the silver-treated "antibacterial" ones.
Wool is a good material.
Best Regards,