I'm still not understanding, only intake fans will push all air out the case with guaranteed positive pressure which is what you want. It doesn't need to be sucked out. Cases are really small (80L for big cases) compared to the volume of air even a single 120mm fan can provide (±20L/second) so you'll have no air just sitting around (assuming semi logical placement of this fan) due to turbulence introduced by the components in the way.
Internal air circulation, there is no guarantee that air comes in and out like an assembly line, you can have some hot air just doing circles in the case while some cooler air escapes out doing nothing. Although the inside of a case won't become a perfect pressure sealed container, air can build up and compress resulting in (whatever unit quantity you want to measure in, pascal/psi, liter, moles, whatever) quantity of hot air stuck in the case (you get to an equilibrium where hot air expands its occupying volume, but the case is passively slowly venting air through relatively small number of holes compared to the case total surface area, the rest is contained inside the case structure). Having fans pushing in air and sucking out air creates the assembly line (or aka chimney) effect, carrying out the hot air.
Edit: I personally think those cases that have fronts and then immediately alongside them have exhaust fans are completely useless like the following on the left with purple fans:
The only time it makes sense is if you have a front/side radiator, which you then don't want to circulate in hot air that was just extracted from the cpu: