If tariffs, quotas, and subsidies each cause net welfare losses, why are they so common, especially in agriculture, among the industrialized countries such as the united states and the members of the european union?

To protect domestic businesses.

Let’s think of the USA and China:

If:

USA steel factories produces 1 steel girder and sells at $1000

Chinese steel factories produces 1 steel girder and sells at $500

—— If there is NO quotas, tariffs or other protectionisms, then the most rational thing is to purchase the Chinese steel girders. Harming USA steel factories.

—— If USA raises tariffs: Puts 50% tariff of Chinese steel
- Then Chinese steel, for USA consumers would cost $750. Lowering USA’s demand for Chinese steel but increasing USA consumer’s demand for USA steel.

They can increase the USA’s economic welfare as many domestic steel-extracting factories and their employee’s are protected/benefitted. Though, it may harm some manufacturing jobs.

Well, in the end it depends on the scale of those trade barriers.