Sweat cools the body via evaporative cooling. In order to do its job, it needs to evaporate.
That is not going to happen effectively if your armpits are buried under much typical "everyday" clothing, especially typical male office attire. You are simply going to accumulate armpit moisture at a much faster rate than it can evaporate. It will eventually get a little smelly thanks to the byproducts of normal healthy bacteria, which (depending on culture) many would rather avoid.
If you are shirtless, or wearing some sort of sleeveless shirt? Or some kind of moisture-wicking shirt? And/or sitting in front of a fan that's blowing air through your sleeved shirt? Then yes.... armpit sweat can help you stay cool, and for maximum cooling you should avoid antiperspirant. That's why i.e. athletes and such wouldn't wear it.
However, for many of life's other clothing situations your armpit sweat won't help you stay cool in any useful way. For these kinds of situations, that "clinical strength" stuff is a godsend to me.