There are quite a few advantages.
Taking a look at a typical superhet (up to the IF):
The input signal at the RF input is small (as low as -122dBm in some narrow band voice systems I have worked on - that is about 6.3fW)
To amplify a signal at a high RF (say a few GHz) is expensive compared to doing that amplification at a lower frequency. A few dB of RF gain is usually sufficient to process the signal up to the IF stage.
The input filter bandwidth has to be such that it is less than the channel spacing (usually less than the output bandwidth) so it is easier to implement.
The image rejection filter bandwidth is set by the local oscillator frequency (at RF +/- IF), so choosing a relatively low IF means that image rejection is relatively easy to do as well.
The IF amplifier is usually where most of the signal gain is done at a relatively low cost and low complexity (compared to trying to do that at higher frequencies). The filter prevents bleed through and sets the signal bandwidth to the information bandwidth.
Another major advantage is that everything after the mixer is fixed - no adjustment necessary during normal operation which is why the dynamic signal range can be high. I have not shown the AGC (just about always present) but that is also a fixed piece of (dynamic) circuitry.
An improvement is the double superhet (2 IF stages) which I worked with decadees ago and they are still highly popular.
There are direct conversion receivers but they suffer from a number of issues, in particular dynamic range of the signal.
[Update]
In response to the comment, there are wide dynamic range direct conversion receivers (one possible source listed); these have been around for some time and are often found in SDR setups.
A purely hardware approach favours the superhet.