I've learned it is to flush the papery particles and avoid a kind of paper taste to your coffee. When i use hot water to flush i can also kinda smell the paper, the hot water also heats up my filter holder at the same time.
This is true, but it also helps to wet the paper so that the coffee goes into the cup/carafe. By wetting the paper when you go to pour in the first bit of water it’s not the strongest coffee being absorbed into the paper. It also helps to loosen up the fibers and get everything settled rather than having it settle while there’s coffee in there. I also use it as an opportunity to ensure I’m getting the paper to stick to the sides so that if I accidentally pour on the side of the filter and down the cone it will still interact with the coffee grounds.
As you said too, if you use a porcelain cone it helps to heat it up so you can maintain brew temps. Most plastic cones may not see this benefit though.
Help the paper stick to the dripper body, remove manufacturing dust, and reduce/remove possible paper taste. Using hot water also helps pre-heat the dripper reducing heat loss during the brewing process.
With the filters I use, it removes the 'woody' aftertaste from the coffee. It worked on an old philipa as well as with the moccamaster I now use on workdays.
Don't use paper filters, but I'd assume to avoid channeling in the coffee grounds. Water will always go through the path of least resistance, maybe by having the entire filter wet you lessens the chances of overextracing some parts of the grounds and underextracting others.
I did read that some people do it to remove paper taste, but that seems a little weird. Edit: i was wrong.
It's exclusively to remove paper flavor. There are microparticles stuck to the filters you don't want in your drink.
Channeling on the other hand happens when you have irregular grind size and distribution in your grounds. Stirring them pre-pour and pouring gently in consistent motions helps with that, as does a proper blooming phase. Wetting the paper has no effect there.