I'm assuming you mean instruments
and microphones excepted, because many high-end recording microphones cost $1000 and up. Yes, there are legends of a few albums being recorded with only a few SM57 (a $100 mic), but they're the exception - and most such albums aren't generally regarded as audiophile-quality.
But regardless, even just the input transformer on most mixing consoles costs at least $100. And many extremely high-end consoles use discrete opamps which can get really expensive. There's also a lot of tube-based outboard gear in studios.
Sure, you could build a mixing desk with only $2 opamps and no transformers, no tubes, etc. But that would sound bad. Unlike the audiophile world, recording isn't about doing everything possible to prevent distortion - if it was, all recording would be done with calibrated measurement microphones and other various lab equipment.
So how can distortion be good in recording if it's bad in reproduction? A few reasons. IM distortion, for starters - distorting every channel individually is going to sound much different (and in most cases, better) than distorting the mix of all the channels.
But also, in recording, the distortion is finely tuned to the exact song, by someone who gets paid hundreds of dollars an hour because they are very good at it (and yes, good at getting it to sound even better on a variety of different systems). A recording engineer can use exactly whatever mic preamp they think will sound best for the song. Yes, audiophiles do tend to adjust tiny settings for each song, but not to the degree that recording engineers do - no audiophile is going to own 20 different amps and switch them out for different parts of different songs (or at least not on a regular basis).
Recording engineers can also do so on an individual channel basis - use one preamp for the vocals, a different one for the large-diaphragm condenser over the piano, another different one for a small-diaphragm condenser pointed right at the piano hammers, etc. Unless they're using Dolby Atmos or some other multichannel format, an audiophile doesn't even have that option, no matter how much they enjoy tweaking minor settings.
So no, the signal path is certainly not way less than $100 worth of components - and it wouldn't sound nearly as good if it was.