It is a matter of the expected user knowledge and the intended market.
Any good DMM will specify very clearly what is the operating frequency range, the measured signal characteristics, and the DMM parasitics. Some DMMs even have 'fast displays' that operate at a different bandwidth than the slower digits, these will be clearly specified in the marketing material itself. Some markings will only be understood by the experienced user, e.g.: "True RMS".
So it is not true that DMMs don't specify these characteristics, look at the low-end general purpose Fluke 114 marketing pamphlet. It is clearly seen that it is designed for signals below 1kHz. Although they do not specify loading impedance, you can go to the user's manual to find that. (BTW: the models just above this one, 115 & 117, measure capacitance by applying a known charge and measuring voltage, these do not use a frequency sweep).
But this is a general-purpose low-cost (for a Fluke) automotive and household multimeter, it is not really intended for the electronics professional. If you look further up their extensive and expensive DMM product line you will find more detailed and specialized specifications, geared towards one market or another.
When it comes to an inductor or capacitor these are far from ideal components, their actual value will depend on many factors. Temperature, DC bias, applied signal magnitude, and yes, test frequency. Depending on the application some of these factors will be important while others will not. Test instruments are designed with these factors in mind.
That is, the instrument specifications will strongly depend on the intended market. The market for most LCR meters is not your common household as it is the case for the cheaper DMMs. You cannot really compare a $10 disposable multimeter with a $6000 professional LCR meter.