Do they lower government interference, or do they just change the face of the government interference? I'm all for free trade, but free means free. How much needs to be specified other than, "I won't stop your sellers, and you won't stop mine. All other laws apply."
Tariffs are taxes that exert more government control over the economy. Same with quotas. Removing them or lowering them reduces government control of trade and the economy. The more economic freedom a country practices the more wealth they will accumulate. There is also a solid correlation between the amount of personal liberty people enjoy and the amount of economic freedom a country practices. Since WWII we have significantly reduced barriers to trade and our economy and wealth have increased dramatically.
You said that whacks better than me!