Would be better with XLR, but anyway, the jack is the standard that was used in the very first electric guitars.
I'm not sure why they chose that one at the time, but it was the same kind of connection used in telephone boards, so it was already a standard for audio long before the invention of electric guitars. The jack was invited in 1877. Makes sense to use something that already existed and had proven to be reliable and available.
The reason they're still used is for backward compatibility. Other cabled instruments and microphones have changed standards through the years, but because guitars need to be paired with all kinds of amplifiers and stomp boxes from various manufacturers from different decades, it's impossible for one brand to change the standard.
A curious fact is that the 1/4 jack is the longest running connection standard.
With many professionals using wireless cables these days, it could more easily be changed, but at the same time, since going without a cable also removes many of the issues with the jack, there's really no need to change it.
An unbalanced cable has two wires. A ground and the signal. The audio is the difference between the two. A guitar cable is unbalanced.
A balanced cable has 3 wires. A ground, a signal (+ hot) and a signal with opposite polarity (- cold). The receiver will flip the polarity of the cold signal and add the two signals. The result is that any interference that happens in the cable is also flipped on the cold signal and thereby cancels the interference on the hot signal.
Put in like math: let's say your audio is 3x and noise is 0.5y
An unbalanced cable would deliver 3x + 0.5y =noise being added to the output.
A balanced cable would deliver "hot" 3x + 0.5y and "cold" -3x +0.5y. The receiver flips the cold resulting in 3x+0.5y +3x -0.5y =6x + 0y. This can then be divided by 2 resulting in the correct 3x and no noise.
Yeah, a guitar output is a mono unbalanced two wire 1/4" TS jack.
Of course there are people who make guitars with custom wiring, but the standard is TS. 2 wires: tip and sleeve.
You can use a stereo/balanced TRS jack with 3 wires,? (Tip, Ring Sleeve) but only because those are sort of compatible with TS. It won't actually be balanced.