Finiky guys will vent them to the factory point so disturbed air doesn't mess with the carbs operation. Yhey can be routed into the air filter box per Hondamans book.
The factory attached hoses and routed them behind the engine in front of the swing arm. This prevents (or greatly reduces) dust, dirt, and insects from getting inside the carbs and mucking them up.
Most of the SOHC4 carbs have those two hose nipples as well as all four overflow drains sourcing atmospheric pressure to fuel surface inside the carb bowls in normal operation.
The bowls need atmospheric pressure so fuel can be pushed through the fuel jets when the engine cylinders make vacuum at the opposite end of them. Routing to the air box will upset the jetting at worst, or increase dust, dirt and insect fouling to the carb bowls.
The same vacuum source is applied to the air box. If you put the same vacuum source at both ends of the fuel jet orifice, the flow is stopped. Since not all of the vacuum is applied to the air box, partial vacuum will reduce the fuel flow through the fuel jets, as they normally get full atmospheric pressure, not a reduction in pressure sourced from the engine cylinders.
Routing only the two "vent" nipples to the air box, would at the very least create a positive air flow through the bowl chambers sucking air into the air box, from the carb drain tubes, which are normally located at the bottom of the bike, sucking road grime into the bowls and eventually the air box.
I can't imagine why Hondaman recommends this modification. As, it is just plain wrong for designed carb operation and keeping the inside of the float bowls uncontaminated.
