ok, it's just a single datapoint, but motocross racetracks in New England, already built in the woods away from civilization, started requiring mufflers about 50 years ago, early 1970's
In the case of gasoline cars, there are mechanisms for controlling intake air, recirculating exhaust gas, and filtering emissions directly out of the exhaust gases. All of these impact carbon emissions.
These defeat devices allow drivers to modify some or all of these attributes in favor of gaining engine performance.
A misfire is raw fuel being expelled.
They can lead to the popping sound you're describing, but they don't always, and they're far from the only cause, and muffler deletes aren't necessary for those either. Unburned fuel hitting oxygen in the tip of a hot exhaust and immediately burning is the direct source of the noise, and causes for that are numerous.
I saw this analyzed on a Chevy Silverado that would randomly misfire. Everything else checked out: fuel pressure, spark plugs, firing timing, and fuel injector pressure. The remaining item: muffler delete.
But the incomplete ignition of fuel can occur in both stock and modified vehicles. My car is completely unmodified, but can very easily have a low quiet popping noise during downshifts. With e removal of my muffler, it would be quite loud.
A modified engine can do this to a much greater extent, depending on the modifications. Some do so intentionally with what is known as a "burble tune", which is quite annoying in my opinion. It is inspired by rally cars that would intentionally inject fuel during the exhaust stroke and fire the spark plugs to keep exhaust driven turbines spinning even when under deceleration.
The parts may even be more efficient and less polluting, the government bureaucracy everyone here is worshipping doesn’t give a rats behind.
Except I had all sorts of aftermarket parts in there from years of repairs, none of them with the all-important California CARB seal of approval on them, so even though it blew clean, it still "failed emissions" and I had to sell it to someone out of state. I'm still bitter about it.
Further, and most people don't know this is a thing, you CAN tune your car as much as you want and have it certified with all of those parts as a one off for about $5,000 and a six-ish month wait. This is how you can legally import overseas vehicles and get a California title and registration, but it's $5,000 per test, and it usually takes more than one if you aren't super prepared. After the certification the entire engine (including all modifications) are regarded as that being the SMOG compliant form.
One other major loophole is kit cars; SB100 allows for non-SMOG vehicles to be built as a kit. Not everyone's cup of tea, but you can build things like the Superlite GT-R [0] or SL-C [1] and never SMOG it.
You are barely correct. A filter alone is insufficient to be an issue, but a cold air intake will mean you don't pass smog in CA.