Your main point is correct — no general-purpose writing system has ever been pictographic, not even Egyptian hieroglyphs. But all of your supporting points are wrong.
Egyptian hieroglyphs were in use for about 3600 years, and as other commenters pointed out, Egypt stopped using them because they were conquered by Rome, which then imposed Christianity — which banned a different kind of "icon", killing the hieroglyphs as a side effect. Also, far from being "icons" in the UI sense, Egyptian hieroglyphs were primarily phonetic, although they did have ideographic components — less so than Chinese characters (which are logographic, but only about 4% of them are pictograms) but more so than the Latin alphabet.
The Latin alphabet, which is a modified subset of the Egyptian hieroglyphs (via the proto-Sinaitic and Phoenician abjads and the Greek, Etruscan, and Old Italic alphabets) has been in use for 2100 years, about 1500 years less than the hieroglyphs.
If we're still using the Latin alphabet around AD 3400, your argument from observed adoption that alphabets work better than pictograms would make sense — if hieroglyphs were pictograms, which they mostly aren't.
Every invention of writing except the khipu started out pictographic: Chinese characters (which have been in use since the Shang dynasty a bit over 3000 years ago, contrary to what you seem to think), Sumerian cuneiform, Mayan hieroglyphs, and Egyptian hieroglyphs all have clear pictographic origins. But all of them developed phonetic components in order to expand the range of language that could be written, and those phonetic components came to dominate the script almost immediately, to the point that none of them have an identifiable pictographic-only period in archaeology. In fact, as the numerical nature of the decoded khipus and much of the early Sumerian tablets suggests, logograms for abstract concepts such as numbers may have been in use as early as pictograms or even earlier. So, the actual history supports your idea that systems relying entirely on pictograms have very limited applicability, even though it has nothing in common with the history you imagined supported that idea.
On the gripping hand, maybe computers are not the same medium as clay tablets and printed paper, and so maybe past experience is not entirely applicable.