I do 100% understand what you’re saying, and for most setups you’re absolutely right, that’s about all most folks can do. But with a heat lamp the “cooler side” of the brooder isn’t really much cooler. It’s still being heated, you know? Unless the brooder is the size of some bedrooms, the brooder temps away from the heat lamp still won’t get down to ambient temperatures. Folks who brood chicks in a bathroom, with the heat lamp and chicks in the bathtub, usually say that they were glad to get them outside because the bathroom (the entire bathroom) was way too warm. (@bruceha2000, I’m talking about you, for one!I always understood those old recommendations to be the temperature right by the heat lamp, with the rest of the brooder cooler. (My sources: a selection of hatchery websites, state cooperative extension sites, and books from several decades ago that were based on such guidelines.)
Using a heat lamp to warm just one area, while the rest of the brooder is cooler, lets the chicks move back and forth between cooler and warmer areas, similar to what your heating pad allows.
But that requires quite a bit of space, more than most people are willing to provide in their house (or even in some chicken coops!)

When my chicks move out from under Mama Heating Pad, their “cooler area” is definitely way cooler. It’s truly the ambient temperature in the rest of the brooder, as low as 20-30 degrees. They spend most of their time out there, content and growing and feathering out quickly. And their brooder isn’t huge, as you can see. These are Silkie chicks at just a few days old. The ambient temperature was 29 degrees.