Why can unreactive metals be found as pure metals but most require a chemical reaction to extract them?

Really define unreactive metals. Iron is not considered reactive, but it is not found as elemental iron in nature. Gold is found as elemental gold, as is true of some of the other precious metals. But gold is not simply going to be shaken out of a pile of dirt in most cases, so they react those metals with other compounds to make them more soluble, and extract them.

In many cases, selective extractions can get the metal you want and leave other metals behind.

You also are probably aware that there may be only ounces of a metal in a ton or an ore, so extractions are used to remove the metal from the dirt and other things in that ton of material.

An unreactive metal, by definition, tends not to form compounds with other elements.