Would it be crazy loud if I just ran straight pipes out the back from the headers?

I don't know about what other cars had.
I have seen other cars use exhaust systems like an E body Cuda and other MoPars.

I was just helping a friend with a 69 Mustand, 390/4spd. The exhaust had (for lack of better/proper words) glass packs under the rear seats and a muffler between the gas tank and rear seat back.
I noticed even my old 318 Duster, dead stock, had a muffler under the rear seat and a resignator (sp!?) in the tail pipe.
This type of set up can be very effective in sound control.

Most guys that want it quite inside the car refuse to get a longer muffler or one that "could" flow less and end up in there word, suffering under the drone sound. Of course the longer muffler effects sound at the end of the tail pipe and that is what seems to be the supreme No No!