That’s one of the main differenced between pre-mixed flames and diffusion flames.
In burners like oxy-acetylene torches the fuel and oxidizer are blended in proper proportion before ignition and are limited only by propagation rate. That inner core is the limit of the flame wall where the flow rate of the fuel/oxidizer mix perfectly balances the propagation rate of the flame, and that’s where the real action happens. Same thing with Bunsen burners, but the oxidizer is atmospheric oxygen.
Diffusion flames, like candles or the jets on your stove, are different. There you have hot fuel on one side of the flame wall and oxidizer (usually atmospheric oxigen in most applications) on the other. They interface at the flame front and diffuse together to react, so the tip is in fact the hottest point.
As far as the OP goes, you don’t care about flame temperature as much as total heat generation. While the tip is the hottest part, just getting the tips in contact with the bottom of your soup pot isn’t going to transfer as much heat as a larger volume of hot gas.
More fuel burned gives you more heat.
This answer is really general and kind of lousy.
Someone like Anthracite could give you chapter and verse.