What does a drag racer have?
What did the wartime piston engines use?
There's your answer.
Ah, but it's NOT that simple.!
Cam-timing and profile have an influence...you're aware of the 2-stroke's tuned inlet and exhaust tracts?...-So what makes you think the same laws of physics are suspended for 4-strokes?
The above examples both totally ignore any ecomomics or longevity issues, indeed, most of a dragster's potential energy is "!wasted" on crowd-spectacle, as only the most concentrated part of the power is effectively used.
Apart from the fire and noise issues, aero-piston engines have the huge advantage that they are virtually "constant-speed" machines.....therefore, inlets, exhausts and cam-timings can all be optimised to be "in tune" atthe normal operating revs.
This gives you better fuel-efficiency, better power output and longer life. it can also have a marked effect on sound level.
No doubt one of the proper engineers will explain the nuances of resonant-frequencies, valve-overlap,gas-column inertia and the likes.
meanwhile, just ask yourself....if an exhaust wasn't needed, why would manufacturers waste money designing and fitting it?
It's well known that most commercial designs are a compromise of ease of manufacture v benifit obtained....the cynic says they get away with the cheapest and easiest, not the best solution.......hence you get the premium-quality aftermarket items.
Where an engine design indicates, a proper exhaust system CAN, as part of a design, allow the incoming charge to go straight through the "cly"
cooling the exhaust-valve, then, by virtue of pressure-waves, use the otherwise-wasted exhaust energy, to push that "spilled" charge back up into the combustion chamber...in effect, the cylinder is already pressurised before the piston starts compressing the charge.
Apart from watching the pretty flames and enjoying the crackles and bangs, there's no point omitting an exhaust system!