Quite the contrary. The purpose of adding the air is to provide oxygen to the exhaust and since the exhaust is extremely hot ie. above the temperature of ignition of gasoline, any unburnt fuel in the exhaust will ignite. This is similar to "turning on the afterburner" If anything in most cases it will cause increased heat in the exhaust. This system was developed back in the 1970's to help meet emission standards in engines with poor combustion. My 1985 Posche928 has air injection with an air pump pushing fresh air into the exhaust catalytic convertors for the same reason but the catalytic converter system catalyzes the raw unburnt fuel and oxygen that didn't combust in the exhaust manifold.
This air injection system kind of fell by the wheyside when fuel injection came into play. Carbs are really hard to dial in and get to work under all ambient temperatures, barometric pressures, engine temperatures so the air injection helps overcome the shortfalls. Fuel injection comes in 2 standard variants. Closed loop and open loop. Closed loop is for the most part is similar to carburation. It bases it's principals on a direct ratio between air and fuel and usually uses a mass air flow sensor to measure the amount of air entering the engine ,an air temperature sensor and an engine temperature sensor and based on a set fuel map, adds a proportioned amount of fuel. It's a simple system and only slightly better than a well set up carburetor.
An open loop system has similar sensors to the closed loop system plus an oxygen sensor in the exhaust and based on all of the feedback will constantly change the fuel mixture to meet a fixed number signal from the O2 sensor called lambda and the idel number is "1" If oxygen were introduced into the exhaust before the O2 sensor the system wouldn't work and yet there are some systems out there with open loop fuel injection and include air injection like my Porsche but in the Porsche the air is injected right into the catalytic converter which is after the O2 sensor.
So, to answer your question remove or leave alone? If it's working properly and your carbs are jetted properly for the altitude that you typically ride in I would leave it alone. If you're having backfiring issues and your check valves are screwed or your air injection valve is toast, then remove the system. No harm No foul. It's not like you have to meet emmission standards anymore. if for some reason your country requires that you still have to meet emmission requirements then of course you'll have to "fix it" Any licenced mechanic caught messing with emmission pollution controls in Canada would be subject to a fine of upwards of $5,000.