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Let me bring up some technical facts of what actually happens @ different samplerate / Bit depths. There really isn’t any voodoo involved.
You have to break it down into stages.

Part One.
SampleRate in regards to your hardware(Your A/D D/A’s)
The available digital frequency response = 1/2 the sample rate.
So keep this chart in mind
44,100hz = 22.050hz
48,000hz = 24,000hz
88,200hz = 44,100hz
96,000hz = 48,000hz

Now lets say we want to have clean 20-20,000hz recording capabilities. This is what most A/D D/A’s strive for.
All A/D’s use filters on there inputs.
If you are recording @ 44,100hz and are trying to get a clean 20-20,000hz the filter only has 2.05k of bandwidth to do the cutoff. This is extremely tight & near imposable to do transparently. Most A/D’s will cut into the audible realm @ 44,100.

Changing to a higher samplerate allows the A/D D/A’s filter to have a more graceful cutoff slope & get out of the audible range.
44.1k gives the filter 2.05k of bandwidth
48k gives the filter 4k of bandwidth
88.2k gives the filter 24,100k of bandwidth
96k gives the filter 28,000k of bandwidth

This is the main reason to record with higher rates @ the hardware level.

Part Two
SampleRate in regards to processing DSP/Plugins

With added frequency bandwidth you get a few benefits. More natural EQ/filter slopes, less audible aliasing/distortion.

EQ Example
filter slopes extend out based on the Q&gain setting. If you boost the high end @ 44,100 the slope can slam into the 22.050hz limit & not be able to extend out into it’s desired range. = harsh slope. With higher rates filter slopes can extend naturally
Here are some charts of pink noise being played thru an digital EQ with a 16k boost @ 48K & 96K with the exact same settings.

48k=

96k =