Why do LCR meter manufacturers give the details of measurement frequency to us?
They give you the details, because for real-world components there isn't one concrete value; they are all dependent on the operating frequency to a greater or lesser extent.

The best frequency will depend on your application. Ideally it would be the same as your target operating frequency.

For example, if you are measuring an SMPS inductor then a high frequency will be more useful (as your circuit operating frequency is likely to be high), an electrolytic capacitor would be best measured at a lower frequency (as they don't have, and you wouldn't design expecting them to have, good high-frequency performance) and a line-frequency choke would be best measured even lower.