Kinetic energy is 1/2 x mass x velocity squared. So with the same amount of energy, a smaller bullet goes much faster, but has the same energy. You add in less weight that means the 9mm has less of an arc. That is why it was invented. A good shooter can compensate for the arc, but an average shooter will do better with the 9mm.
There are double stacked 45's, but double stacked clips were invented for the 9mm, and work best for the 9mm. In a real life situation, rate of fire is often important. For instance, two thirds of NYPD shots fired at someone two yards or less away missed completely. No one could miss a paper target two yards away, but a real life human, trying to stay alive, is just a harder shot. If you are going to miss two thirds or more of the time, you better be shooting a lot of bullets.
RB highlighted the need for more energy to get through body armor. Given that the 45 does not have the energy needed to get through body armor either, it really is not the solution. Also I should add, that a smaller bullet with more energy will do better against body armor.
A real life possible solution, which did not turn out well, was the FN 5.7×28mm. It has a bit more energy than a 9mm, or a standard .45, and is smaller. 9mm has a diameter of 9mm, .45 has a diameter of about 11.4mm, but a 5.7 has a diameter of only 5.7mm. It was supposed to punch through body armor. From my understanding, it did not turn out great.
A NATO 5.56 will get through body armor, and a 6.8 will get through body armor at a greater distance. Both are meant more for rifles, so would be silly to fire them from a pistol. There is currently not a straightforward answer to dealing with body armor.
What police around here are doing is carrying pistols, usually 9mm Glocks, on their person, and keeping assault weapons in their car. If they encounter someone with body armor, they have to return to their car to get their rifle.