first off, loosing the AI will stop your header pipes from 'bluing'. If you are going to do any performance upgrades to your engine the AI will need to go.
And it is way easier to get at the spark plugs the the tubes for the AI gone.
I see no down side unless you are in an area where they (government) tests for vehicle emissions, then you might have a problem.
The purpose, as you asked, is to inject air into the exhaust stream to complete the burning of the air fuel mixture, much as the pre-catalytic converter cars had the air pump and the tubes going into the exhaust manifolds. Boy thats a mouth full. Pollution control is the short answer.
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