First of all, it's not noise. It IS music, wether you like or not. In fact much of that kind of stuff I don't like it either but I won't go there denying it's music just because of a matter of personal taste. Even if not necessarily liking it, it's very interesting and it doesn't hurt to open the mind and ears a little to forms of music that differ from the traditional.
It's not even John Cage's 4'33'' or works of that sort we're talking about here. The above isn't even a too "Avant-Garde" piece by Schoenberg.
And you can disagree all you want and strongly as you want but Mahler, and now that we're at it Wagner, are clear and pivotal precursors of dodecaphonic and atonal music. That's a fact: they both took the tonal system to the extreme and were both close to breaking it (we can argue Wagner actually did in a specific moment). They put the basis from which the likes of Schoenberg, Berg or Boulez on one side, and Debussy or Ravel on the other, developed their own ways of dealing with the tonality crisis.
Being out of the tonal system doesn't make the music incoherent btw; the serial system is precisely one of the ways to give coherence to this.
Also: not all music has to be tonal. Much of the popular music we are used to isn't (even if it's not atonal either).
The lack of regularity it's precisely what some of this music (which again... it's not noise just because you don't like it ) seeks. To move apart of the musical forms of the past and to avoid repetition. And, though it sounds counterintuitive, to give the composer more control over the final work.
And there's quite a process behind it so no... it wouldn't sound the same if you "randomly press the keys of a piano".
That being said, there's actually aleatoric music. And well, there's also a process behind this... I had to write a piece some time ago.
"All the real musicians"
These composers are all highly accomplished and skilled musicians - much more than me to start with - who pushed barriers and took music to new horizons, even if there's often a snobbish side to such a quest.
Soundtracks from movies, video games, etc owes a lot to these guys and their new and different treatment of music.
And, like it or not, Mahler and the such have A LOT to do with the atonal composers that came after them.
And that is quite the narrow concept of what music is or what should it be.
Not every music seeks beauty. Music as every form of art seeks to express something, and that something doesn't have to be beautiful neither has to aim to be it.
Feelings - or whatever else someone wants to express - can be unpleasant, can be violent, etc... music, and all art just expresses them. To claim that "real musicians" should always looks for "beauty in music" in terribly narrowed minded and even quite naive.