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RMS-DC converters

I have prototyped a low-power embedded device that makes use of the Linear LTC1966 RMS-DC converter. It works splendidly, but the price of this device is a concern ($7 on Digi-Key and has gone up since Linear was acquired by Analog Devices). It uses a delta-sigma algorithm to accomplish the conversion, but I am wondering if the same thing or a decent approximation could be accomplished with an inexpensive MCU. I already have an MCU in the prototype and am thinking I could eliminate an expensive part by moving RMS-DC conversion there. Aside from the cost of developing and testing new MCU code, is there any advantage to having such a specialty component in the design that could justify its significant cost? Is it reasonable to do the majority of signal processing with just the MCU? If so, perhaps the days of such components are numbered.

I should add that I don't need a lot of precision in the conversion. For proof-of-concept, I used simple, passive signal integration consisting of a Schottky diode & capacitor that worked OK.

Datasheet: https://www.analog.com/media/en/technical-documentation/data-sheets/1966fb.pdf