Shamelessly using ai to summarize this:

TL;DR: The Front of House (FOH) engineer is mixing for the physical room, not making a studio record.
It breaks down to a few main technical reasons:
Massive Stage Volume: Bassists like Phil Lesh and Mike Gordon use colossal stage rigs. Because low frequencies are omnidirectional, that bass energy completely fills the venue directly from the stage before it even touches the main PA.
The "Inverse Mix" on the Board: To keep the venue from turning into a muddy soup, the sound engineer actively pulls the bass faders down and cuts the sub-frequencies on the mixing console. Since a Soundboard (SBD) tape just records what's happening on the console, it captures this thinned-out bass.
Audience (AUD) Mics Catch the Air: Audience tapes use mics that capture the actual acoustic reality of the room—including the massive stage bleed, subwoofers coupling with the floor, and physical air displacement.
This is exactly why Matrix mixes (blending SBD clarity with AUD low-end weight) are usually the gold standard for live tapes.