Int isn't converted to spirit, and spirit is not supposed to be static.
Int/str/agi are the main stat. Which one of them shows up depends on your spec. If I'm an enhancement shaman, my gear will show agi as a stat. If I now respec to resto, the agi will morph into int.
Spirit is a stat that you will not find on your regular armor. It'll be exclusive to a few select slots such as rings, neck, trinkets and such.