Is using a mixer preferable to having a separate recorder for each mic?
Well, the two aren't mutually exclusive, but we're not talking about separate recorders. So I also want to clarify what Alcove said:
On a "professional" shoot the production sound mixer will record each mic onto a single audio recorder separately...
If, for example, there are three actors and three wireless systems, plus a boom op, we'd be talking about four individual sound recorders floating around the set. That's too much to handle, and there's no way for the PSM to monitor that many devices in any practical way.
What we're actually talking about here, and what I think Alcove meant to say, was that the PSM will record each mic onto an individual record
track. There are a few ways to go about this:
Using a mixer such as the Sound Devices 442 allows the PSM to send a mix of the four inputs to camera, to video village, etc. The 442 also has direct outputs for each input, meaning it has an isolated copy of each input signal that is sent out of the mixer. Those direct outs can be fed to a multi-track recorder like the Sound Devices 744T.
More current offerings from SD (688, 644, 633) combine the mixer and the multitrack recorder into a single device, so you could have 6 mics coming into the mixer, recorded to isolated tracks, plus a mix recorded to a master stereo track pair, plus outputs from the mixer sent to camera, video village, etc.
Those are for bag work. On larger, cart-based productions, you may have a standalone mixer that feeds direct outs to a computer for multi-track recording through a program like Boom Recorder.
There's a catch here, though. Some of the higher-end wireless systems (have like Zaxcom) have wireless transmitters that also record the signal. This provides a failsafe, though, and is rarely used as a primary source. It's a backup in case of transmission interruption.
I see a lot of amateurs, and a lot of low-budget folks who work alone, using small recorders planted on actors, or for weddings on the bride, groom, and priest/pastor, and let them roll unmonitored. This is clumsy and unreliable. I'd never want to trust my sound recording to something I couldn't monitor the whole time. Tascam makes a small recorder that is designed to run as a throughput from some wireless transmitters, between the lav and the transmitter, but again that's just a failsafe and should not be the primary or only source of recorded sound from that mic.