IR LED in TV remotes run 30 to 40khz. I have run those to 60khz at 25% duty cycle.
I have run LEDs way above their maximum current, for a short duty cycle. Some LEDs have that type of data in the sheet but most do not. Lazer or IR might have the data. Most LEDs for indicators will not because almost no one uses them that way.
Here is some data for a 100mA LED. It turns on or off in 15nSeconds. TSAL6200 Vishay
More data: 100mA all day long, 200mA at 50% where Ton=100uS Toff=100uS and 1.5A for one pulse at 100uS.
Another page: They are showing light out verses current for 1mA to 1A. (left side)
Right side: shows time and current.