I'm currently learning about the Superheterodyne AM Receiver and I don't understand why does it use an envelope detector (as suggested here) rather than taking the signal back to its baseband frequency through a local oscillator. That seems more natural to me because it's already using one to take the signal to the intermediate frequency.
The AM receiver could be done with a second Local Oscillator to baseband which would work fine if there was no frequency offset between the transmitter and receiver; otherwise the baseband signal would have an amplitude variation given by the AM in the signal, as well as phase rotation given by the frequency offset and relative delay (consider if the signal happened to be received with 90 degree delay- the result out of a single real mixer after low pass filtering would be 0!) So, the receiver would require two additional mixers driven in quadrature to be able to determine and remove these phase and frequency offsets. The phase and frequency offsets would need to be recovered and removed to intelligibly recover the desired amplitude variation; this is known as coherent demodulation. This can and is often done, at the increase in complexity but also an increase in performance with higher SNR achievable.
Such a frequency offset is inevitable given the transmitter and receiver operate on different reference clocks that can't possibly be at exactly the same frequency, and the frequency difference can be significant for low cost hardware with temperature variations etc. If there is motion between transmitter and receiver, this will add an additional Doppler offset. For software radios where the translation from IF to baseband together with carrier recovery can be done digitally this would likely be the favored approach at the benefit of the flexibility the implementation will provide (and all the other functions that motivated us to go down this path to begin with, certainly not for a fixed AM receiver). For a radio that only needs to demodulate the AM, a simple power detector on the IF output (or depending on the carrier frequency directly on the RF signal) is far simpler and therefore a lower cost, size and power solution.