Exhausts are tuned for power and torque which can improved or even moved up or down the rev range but think of noise as a byproduct.
just to try put an end to keep going round in circles,
manufactures today, do not tune the exhausts to get the most power and torque, the engines are plenty powerful enough, the exhausts and inlets offer plenty of flow. They will tweak the software to get the car in the power band that they want, then they will offer several models with the same engine, exhaust, turbo, etc, in different power outputs, depending on what the customer wants to pay. A prime example of this are things like the Mini Cooper D and the Mini Cooper SD versions which these days use the same everything, but have a different engine map for 150hp or 180hp. This has been going on for years, the old Mondeo I started this thread about was offered in a 1.8 and 2.0 petrol engine, about 120hp versus about 135hp. To make sure that the difference in the engines was notable, despite using the same exhaust and inlet system, they fitted a restricted throttle body to the 1.8 to deliberate reduce the power, so that people would buy the 2.0 thinking they were getting a much more powerful car, but with the larger throttle body on the 1.8 the power difference was virtually undetectable to the driver.
Obviously in the engineering process a decision will be made about a theorectical maximum potential power that the engine and exhaust set up will be capable of, this however will be well above the specs that the car is actually sold with.
Your Golf R doesn’t need to play silly sounds I agree and it could be made quieter with a more restricted silencing system but it would lose some performance all other things being equal. Some of these valves you mention apart from changing exhaust note bypass cats or divert
I don’t have the Golf R it was an example.
The car does not need to play “silly sounds” to make it quieter, but it does because it is already too quiet, it doesn’t need to be made quieter, they have already fitted all the required silencers etc, but customers want there high performance car to sound a certain way and so they have programs which play the sound of an engine that is louder, to keep customers happy, someone takes it for a test drive and thinks the engine sounds super powerful when really it is an artificial sound being played. It’s a perfect example of people thinking a noisy engine is a powerful engine.
The electronic valves, I am talking about are usually fitted to high performance cars, they are a mechanical/more tactile way of increasing engine sound without the piped electronic sounds being played.
They do not bypass catalytic convertors, they are manufacturer fitted and usually bypass if anything a stage of silencers to let more of the engine sound out, or route the exhaust through a silencer that is tuned to make more noise, However, there is no indication from the manufacturers that this increases power in anyway, it is purely done for sound because again, people buying performance cars, expect the car to sound a certain way. but buying a car that makes a racket all the time gets tiresome very quickly so they give you a way to switch it off.
Going back to my example above, they can easily overcome any power loss from an exhaust silencer, by plugging it into the computer again. So say opening the valve in the exhaust did freed up 5 - 10hp the car may easily be capable of 20 - 30 even 50+ more BHP with a software tweak and not touching the exhaust, so the manufacture could just make the car super quiet and then use the software to regain any power losses.
An extreme example of how the customer expects a powerful car to sound a certain way with this piped artificial sound is the new Electric 500 Abath which plays a loud engine sound track in and outside the car for everyone to hear, even though the car doesn’t even have an internal combustion engine.
An extreme example of the cars that can be massively tuned just with software and no engine modifications are things like the AMG C63 and E63 models which can go from ~450bhp to 600BHP+ with software tweaks and the Audi RS6 which depending on the exact engine and year can yield over 700BHP with nothing more than a remap of the engine software from around 500BHP to start with.
My old Punto Diesel sporting with 120 BHP was apparently easily capable of 150BHP with a software update. So at least a 25% power increase without touching the exhaust or intakes.
So just to reiterate the point once more, these days and for a very long time, car makers have not been fettling the exhausts of their cars to squeeze the most power out they can. Even in the highest performance cars where the exhaust is probably designed to a very high standard to get the most out of the engine, there will always be a few extra horse power to be gained in software.
Things have moved on a lot from the 1970s and we are not building race cars or tuning go-karts. You seem to think I am confused by how an exhaust system works…. I am not. 
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