"Even simple harmonies in wider spreads would have been lost as a single concept on an instrument which couldn't sustain the sound. In a sense, they employed what they could, and the options were limited. Alberti bass is meant to aid in employing a textured, harmonic concept over a greater period of time than just playing the chord would allow."
The point about wider spreads of harmony being lost just isn't true. Look at the Mozart D minor Fantasia, for example. Although there is no melody against these figurations, the style of writing is far more in the vein of Rachmaninoff's than any cliched Alberti bass. It covers a large range of the keyboard and the sounds blend throughout this wide range. Rather than use a bog-standard pattern, Mozart experiments with completely different ways of extending a harmony. Composers just weren't being terribly imaginative when they used Alberti bass. Yes, it goes beyond just playing the chord. But it is the most minimal way of going beyond that. It's the laziest style of prolonging harmony.
The classical composers had sustain pedals and such things could indeed sustain perfectly well. There's an oft-repeated claim that the Moonlight 1st movement and the Tempest recitatives do not sound blurred on a period instrument. However, it's a myth. You get plenty of blurring (just not as much as an extremely insensitive pianist can end up with on a modern piano).
"Also, just because a musical idea may include more notes doesn't necessarily make the essence of that musical idea more complex (unless you think only in a very materialistic way in that there might be more quantities)."
Who referred to quantity as a factor? It's not about more notes in the Rachmaninoff but rather the unpredictable intervals used to spell out the harmony. The intervals make it more complex. However, if more notes don't make it more complex, doesn't that imply the kind of thinking that says it IS just a harmony? All of these things contribute to whether the music just says "this is D major" or whether it creates something way beyond that.
"In the Rachmaninov, the original conception probably included many notes all at once, which materialistically must unfold through our concept of time (just like any idea that we attempt to communicate beyond the original conception), and, of course, notation is limited."
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"Alberti bass is lucky as a materialistic idea because its notation is as simplistic as its concept seemingly is, Rachmaninov was not so lucky."
? I've never had a problem reading the notes or understanding a basic triplet rhythm and I've never heard many pianists misunderstand how to play it. What exactly do you mean? What problem is there in Rachmaninoff's notation and how does that manifest itself, specifically speaking? What do people get wrong due to notational issues? I'm a bit confused, because if we think of it as basically just being one single thing that had to be spread out for the sake of realisation, that surely comes back to the idea that it's basically just a D major harmony? But that's what you were saying it goes beyond being. I think the horizontal movement is every bit as important as the way it combines to make harmony. I don't see it as just a single texture that had to be spread out. Had he orchestrated it, I should be most surprised if he replaced all horizontal details with singular prolonged harmonies.
Topic: What I learned during practice today :