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Why some brands don't do LCR meters?
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TimFox:
Another single-frequency instrument with excellent accuracy (at that frequency) is my venerable Wayne-Kerr B221 admittance bridge, which uses a ratio-transformer bridge to compare the unknown admittance (parallel-equivalent capacitance and conductance) to two (each) fixed resistors and capacitors  at 1592 Hz (10,000 rad/sec).
The calibration, even after 50 years, is quite good, due to hermetically-sealed standards and the constancy of integer turns numbers.
See page 10 of  https://www.pa3esy.nl/meetinstrumenten/wayne-kerr/pdf/Wayne%20Kerr%20Universal%20Bridge%20B221%20and%20accesories.pdf  for accuracy specifications, including the range of values for 0.1% accuracy.
The coolest part of this well-designed instrument is the null indication for the bridge:  two cascaded dual magic-eye tubes, which form a wide dynamic range null indicator with negligible delay, for easy nulling.
Due to the ratio-transformers, negative capacitance (from parallel inductance) and admittance (when necessary) can be measured, and a table of reciprocals in the manual makes it easy to compute the inductance from a negative capacitance value at 1592 Hz to better than slide-rule accuracy.
The exact frequency is only necessary for inductance calculations:  the capacitance and admittance only depend on the standard components.
Another of my good bridges is a General Radio "Z-Y" bridge, usable from 20 Hz to 20 kHz, capable of measuring any impedance/admittance.
(The G-R 1620A is no longer in production at IET, but is good down to 0.01%.)
Kleinstein:
With some parts the frequency for the measurement can matter. This are especially capacitors / inductors that are not ideal but have loss  (e.g. electrolytics, X7R). This makes the capacity / inductance frequency dependent.

A larger frequency range can improve and the measurement range, but not directly improves accuracy. It is more that a limited frequency range / single frequency may allow for better accuracy in the range that works well (not too large or small). The old style bridges were often fixed frequency and can still be very accurate.
A frequency range can still be handy, but the higher frequencyies are somewhat limited: the parts may no longer behave like a simple inductor / resistor or capacitor but one would need a equivalent circuit with more parameters to measure. So one may need more the a LCR meter, but an impedance analyzer as a more general instrument.
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