The receivers for LiveATC and the like are frequently somewhat compromised in terms of quality and location. This can cause poor quality reception depending on the location and distance away of the transmitter.
The radios and antennas on both the aircraft and for ATC are not only of much higher quality but are also positioned as perfectly as possible so as to maximize Tx/Rx performance.
All that to say, the pilots and ATC nearly always experience more clear comms than the general public has access to.
Not long ago I took a short trip in a small Cessna (I think it was a 152). The audio quality in the headphones wasn't any better than what I hear on those ATC YouTube channels. I didn't understand a word of it (well, that's not quite true, I understood some words here and there; not nearly enough to be able to safely fly).
A Cessna 152 is not an airliner, obviously, but I would think audio quality shouldn't differ all that much between them.
The 152 could have had a 40 year old radio or a crappy antenna. Who knows. As you pointed out - that 152 is subject to a lot less maintenance scrutiny than commercial airliners are.
The other thing that plays in here is that ATC language is very highly standardized. In any specific phase of flight, the pilot will generally know what to expect next from ATC. This allows them to discern instructions (and read them back for verification) even if the signal is weak. In situations like these, ATC may seem completely unintelligible to people not used to ATC language and patterns.
From my experience as a small plane pilot, radio comms is almost always quite clear. The antennas and radios are aimed “at the planes” not at receivers on the ground, after all.
The radios and antennas on both the aircraft and for ATC are not only of much higher quality but are also positioned as perfectly as possible so as to maximize Tx/Rx performance.
All that to say, the pilots and ATC nearly always experience more clear comms than the general public has access to.