In most cases True RMS response is better than the simpler rectifier value response.
The main reason to still have the simpler AC version is costs. The old style analog RMS chips are still relatively expensive. It is the relatively new digital RMS as part of the chip set that makes it affordable also at the low end. If the chip set uses an SD ADC chip (the more modern alternative to old style dual slope), the extra effort for the chip-set is rather small, especially for only limited bandwidth.
So far I don't know a DMM chip set with fast digital RMS included, but this is likely just a question time and maybe power consumption.
Another odd case are (old) service manuals for aviation and military that sometime still call for a meter that shows the average of the rectified value. So these explicitely don't want true RMS. AFAIK Fluke has a militry version of a meter that intentionally changed from true RMS to rectifier response, using the same RMS chips, but dropping a capacitor and a resistor change.
The old style non RMS meters can also fail at the high frequencies. One point is the input divider that needs matching parallel capacitors to get accurate higher freuency (like > 1 kHz) readings. With the higher frequencies the divider is set by the capacitors and not the resistors.
Even old analog meters with just a diode rectifier may fail with higher frequency AC: my old analog meter fails big at some 50 kHz showing near full scale on most ranges, in cluding 900 V

.
A cheap meter without trimmed capacitors may as well also use a slow, lower power active rectifier and amplifier, as the higher frequencies would not be accurate (like +-10%) anyway. A reduced BW also comes with less noise.