For the engine, gunking up is the least of your problems. The scratches you would get inside the cylinders would have about the same effect as losing your piston rings; oil blow-by, loss of compression, and generally not allowing the pistons to do their thing. This on top of your other issues.
For the cabin, they make the air a little nicer and, more importantly, keep the grit out of your blower motor and your interior. My car lacks one, and you can imagine how dusty my dash is.