Remembered by whom? There are people to this day who claim to trace their ancestry, patrilineally, to Chinggis (Genghis) Khaan. The "Mughals" referred to themselves as "Gurkani", "in-laws" of Chinggis Khaan, before even their patrilineal descent from Timur, a conqueror of comparable ability. Very, very few rulers have such an immense prestige attached to them as the Great Khan.

Meanwhile, if you read Middle Persian sources, you will often come across mentions of "Alexander the Accursed". The 9th century Zoroastrian authority Adurfarnbagh-i Farrokhzadan writes, for example,

Be it known that he (the prophet Zartosht) had predicted with full details and in concatenation all the circumstances as to how the Kayanian Vishtasp, King of Iran, and his innumerable army would obtain a victory over (the Turkish [=Turanian] King) Arjasp and his hosts, and over other (kings). Similarly had he made revelations about King Vishtasp's supremacy over rulers of other countries ... about the events which would happen in successive ages; about the doers of harm to his religion, such as Alexander; ...

From book 4 of the Denkard, a 9th century compilation of older tradition:

The Ashkanian government (i.e. the Arsacids, or Parthians) got the Avesta and its commentary which from its (original) pure (and sound) condition had been, owing to the devastation and harm3 (inflicted by) Alexander and his general of the plundering Aruman [Roman] army, separated into parts and scattered about, to be copied out. And any (work) which remained with the Dasturs for their (own) study and the writings subsequently obtained in the city were ordered to be preserved and copies of them to be made out for other cities.

Book 7 of the same:

3. Even after the devastation which happened owing to Alexander, those who were rulers after him brought back much to the collection from a scattered state; and there are some who have ordered the keeping of it in the treasury of Shapan.

...

7. Also Alexander of the devastators, as it says even this of him in revelation, that in those three winters, which are of like purpose (ham-ayazako), that Aeshm would set up a deadly king in the impenitent world, who is the evil-destined Alexander.

Book 8:

And after the devastation occurred, owing to the evil-destined and raging villain Alexander, there was not so much of them recovered as would be possible for a high-priest to preserve.

And from the Book of the Deeds of Ardashir:

(6) And Sâsân was a shepherd employed by Babag, who always remained with the horses and cattle (belonging to the latter), and he was (descended) [3] from the line of (king) Dârâb, son of Dârâê. (7) During the evil reign of Alexander, the descendants of Dârâb privately lived in distant lands, wandering with Kurdish shepherds.

Indeed, they hated Alexander so much they attributed to him the destruction of vast amounts of written records of their scriptures, which is very unlikely indeed, given that the Avesta is unlikely to have been written down before the 4th-5th century AD. In fact, Alexander was in the post-Sasanian age sometimes invoked in comparison to the Muslim conquerors, as an evil king of the past they had overcome, as they would overcome (or so they believed) Muslim hegemony.

So, why do "we" (Westerners) remember Alexander as valiant and so forth? Because through the construction of "Western Civilization" we consider him, as a part of Ancient Greece, to be part of our legacy. We inherit a literary tradition where he is praised by generals, where works based on hagiographical accounts of his life and deeds flourished, where the exaggerated and idealized relationship between him and Aristotle, the quintessential thinker of "Western Civilization", is promoted. In one traditional view of his conquests, he brought amazing Hellenic culture to the uncivilized, barbaric East, and defeated the despotic, wicked and totalitarian Persian king. And his conquests were an irreplacable part in the construction of the narrative that leads to the glorious Roman Empire, to which so many Western polities have done their utmost to trace their origins. This is just further enhanced by the Biblical narrative of the great, glorious, just king Cyrus, whose wonderful empire had, in this view, fallen into decadence by the time of Darius III.

It is really all a matter of perspective - in Romania, you will find a tradition commemorating Vlad the Impaler as a great prince who protected them from the Turks; Turkish nationalists celebrate and exaggerate the conquests of the Ottoman Empire, so demonized and dreaded by Christian Europe. It's a matter of perspective, and what we choose to remember about historical events. One can only hope that more critical perspectives on historical figures and realms will become the norm.