The 2nd and 3rd posts are correct.
> You have to factor in tension and flexibility as well. With two strings, tuned to the same pitch since that's what we're talking about*, the one with larger gauge and mass has also more tension and less vibrating amplitude.
Yes. String excursion also affects output, otherwise the output wouldn't rise the harder you play.
> balancing the tension goes in a direction of unbalancing the tone and loudness of the strings.
It can help too, the jump of gauge from D to G is smaller, so the tone progression improves there, helping make the tone of the G more consistent with the others, this is a common complaint.
To help with volume pickups can be tilted, however heavier AD strings may be due to neck radius and flat pickups, but then of course looser strings have more excursion which raises output and compensates, so might as well go with a more ergonomic and playable equal tensions.
> Those 50-70-85-105 and 45-65-80-100 sets are not on the market for nothing
At some point many decades ago traditional gauges were chosen, based on old technology, then a commercial vicious circle of demand and supply kept the tradition going. If every new bass has traditional gauges as stock that's what most players get used to right from the start (new players rarely question gauges), getting accustomed to the feel and tonal change across a set, then that's what they want to buy later, so that's what is provided by manufacturers with pre-packaging costs and shops with limited shelf space, so that's what players buy ... and the cycle goes on, it's hard to break but Kalium are doing it slowly.
> The reason of using them is because they sound better balanced, both in tone and loudness
Tonally that's subjective, it's just a different change of tone across a set, admittedly it can require some re-acclimatisation. Once you're used to it there's actually nothing worse about the tone of a balanced set, you realise it was a case of 'being used to the former'.
> Todays players are a lot more concerned about their own comfort than tone. We all see it. Everybody is moving to a lower tension
There's nothing worse about the tone of a looser string as long as it's above a certain practical limit (which rises for thicker strings, but is around 25-30 pounds), it's just different.
What's happeneing is good, players are realising that traditional 'acoustic contrabass' type tension is ridiculous, unhealthy, not very playable and completely unnecessary, bass guitar is moving towards actually being a bass *guitar* instead of an 'electric contrabass' which is the original concept of the P-bass.
I find so-called 'medium' sets unplayably tight, it's a significant effort to hold a string firmly against a fret, bass should not be only for the strong.
Having used balanced sets i've gone one step further, which is tension falling from low to high like some guitar sets, there are actually many good playability reasons for this but would be too shocking for most bassists. It is however the future and the next revolution after balanced sets.
It's a case of accepting the tonal change of higher, thinner and looser strings, instead of the futile attempt to avoid it.