Your topic question mentions the choke, but that’s not discussed in your details. I’m not going to assume that you know the difference between choke and throttle, so the following may be too elementary to help answer your question. However, it seems to be a sort of confused question, so… maybe not.
The choke is a mechanical device that limits the amount of air entering the combustion chamber. This is normally closed (added air shut off) temporarily for a cold start. In other words, to promote ignition and start the engine at a cold start the mixture is intentionally fuel-rich and starved for air. As the engine warms the choke is opened (either manually or on many engines these days, automatically) to lean the mixture and burn the fuel more efficiently.
The throttle, on the other hand, which is normally controlled manually (“the gas pedal” on a car and presumably the trigger on your hand-held weed-whacker) feeds fuel to the engine.
For many hand-started gasoline engines of this type, the manual choke being closed in preparation for start may also feed additional fuel to the carburetor / ignition chamber, or you may be prompted to pump a bladder or other device to manually prime the chamber with fuel for the starter to engage. As the engine starts, then, there is an intentional surfeit of fuel to burn off, and even without engaging the throttle the machine will run fast as that fuel is consumed. The choke being shut may also cause the fuel to feed abnormally fast (faster than a normal idle, that is) in order to promote the engine warm-up and consequent opening of the choke to enable normal idle speed. (In other words, the “startup fast idle”.)
As for why the engine fails to maintain a normal idle once started and warmed up, that’s a question for a better mechanic than me. Have you checked the air filter? Those can get clogged with the dust and debris that is normally stirred up with this process operation, and too-little air to a warmed-up gasoline engine will tend to stall it out. And people aren’t well attuned to checking air filters.