The tweeter in an engineered cab is not adding artificial highs. It's just reproducing what is already in the signal chain.
Regarding the matching the tweeters output to the rest of the cab, it all depends on how the tweeter's efficiency rating matches the rest of the drivers, IE, if the woofer is 98dB, and the tweet is 105dB, the tweeter has to be padded back 7dB in to be flat (Padding is the term used for resistive circuitry used in a crossover to attenuate the signal). In our illustration, running the tweet full out with no padding will render the frequency spectrum covered by the tweeter 7dB to high. a properly designed crossover will have that padding done via fixed resistors in the crossover circuitry. Then the L Pad (variable resisitor) on the back of the cab is an added bonus. It takes it from that flat position down to off.
Putting in a dome is more than a plug and play. The new tweeter has to be spec'd properly, and the crossover has to be designed for it.