Breather caps good or bad?

I have seen oil breather caps available for cars for years.
I've included an explanation of their purpose coppied form a companies website.

"A breather filter relieves your engine of positive crankcase pressure and recycled carbon vapors from your engine, which cause loss of throttle response due to build-up on the throttle body. A breather helps resolve that problem, by venting the vapors into the atmosphere."

I have a couple of questions.

Is the loss of positive pressure in the crackcase a bad thing?

Will venting instead of recycling unburned vapors throw off the air/fuel mixture that the computer is expecting?

Will it also fail your vehicle emissions tests?

I also assume your fuel economy would fall to as you will be using more fuel/air with less of the recycled vapor in the mix, right?

I fitted one of these filters to my rocker cover just to purify the cold air theory .Honestly, you'd need some very precise equipment to measure a difference in fuel use as I've noticed no change.The throttle body has stayed clean too.
I dont think your emmisions are tested from within the engine bay, are they?!
If the slight drop in 'possitive' crank case pressure -due to these breathing filters-was a problem alot of race car engines would have self destructed as a result.