What the Heck is this Hose ?

When the PCV valve gets stuck closed or restricted by crud, any blow-by pressure simply flows back out the blue line into the intake tube. This can also happen under wide open throttle conditions when there is not enough engine vacuum to "operate" the system or if the engine is worn creating more blow-by than the system can handle.
In the shot below note the left yellow arrow. It's pointing at a drop of engine oil at a place that technically should be dry. This could be caused by any or a combination of the situations mentioned above.
Continued operation in this state allows this oil/crud to enter the IAC system since Toyota was thoughtful enough to put the IAC inlet at the bottom of the T-body (center arrow).

Opening the hose between the valve and the t-body would create a full on vacuum leak.
Best to leave the PCV system to do it's thing.