Interesting idea. First, lets debunk the errors.
JAKEWILSON-- "It's been attempted many times and failed just as many."
Selective breeding over thousands of years? No, what RMcD94 is proposing has never been tried. By anyone. Ever.
"This is because people a.) aren't very good at selecting traits that are actually relevant to survival."
Tell that to the Spartans.
"b.) a state or tribe doing this sort of thing won't survive long as the effort put into it is mostly a waste of resources."
THINGYMEBOB-- "Never going to last for long. Basically, the tribe that pratices this will be pretty small and will find their hunting land/farm land appropriated by the larger, hungrier tribe next door."
Two other things you can explain to the Spartans. While their society is extinct now, it lasted from c. 750 BC down to around 371 BC-- a period of over 400 years. The Golden Age of Thebes, by comparison, lasted for about a single human generation.
MALICE-- "If eugenics had any validity then why hasn't anyone heard of Albert Einstein's parents or any of his children?"
Simple. Because Einstein wasn't the product of eugenics. His phenotype contained a lot of random genes that just happened to combine in a pattern that, with his unique upbringing, resulted in genius-level intelligence. But genius isn't just a matter of genes. Upbringing & random chance each play an important role. The goal of eugenics is, over time, to bring the phenotype-- the exhibited characteristics-- into conformity with the genotype-- the inherited characteristics. The minimum amount of time involved, depending on species, is on the scale of hundreds to thousands of years.
"One other example worth considering was the Lebensborn programme... End result? Children...had higher rates of infant mortality, physical handicaps, intellectual disabilities..."
Possibly because of a lack of nurture. Possibly because the selection criteria used by the Nazis was, to put it mildly, unscientific.
WINNER-- "Depends on what kind of things would these people find desirable. If it was just physical strength and other factors commonly associated with male dominance, the society might actually lose a lot of geniuses."
The Spartans, who are probably the people who've tried this the longest, found that they had more highly competent generals-- a few of whom were certifiable military geniuses-- than they could use, so that they ended up exporting generals all over the Mediterranean world. And they weren't selecting for intelligence-- merely physical fitness.
SIMONBP-- "Human intelligence is...a highly complex combination of genes that are not terribly predictable. ...final intelligence is a function of upbringing..."
Precisely correct.
However, the Spartans had some problems with their program. One huge one was the extreme conservatism that their society engendered, which rendered them unable to adapt to the light infantry tactics practiced by Iphicrates at the Battle of Leuctra, which annihilated an entire Spartan battalion (1 out of 7 in the whole Spartan Army); or the oblique-order tactics practiced by Epaminondas at the Battle of Leuctra, in which the entire Spartan Army in full battle array suffered its first-ever defeat. These 2 defeats tore the heart out of the Spartans, rendering them unwilling to accept the extreme hardships mandated by the Code of Lycurgus that had given them their unique way of life, & the decline of Sparta set in. So we're left with a question: "Does a eugenic breeding program engender in a society that practices it such extreme conservatism that it renders the society inflexible, & unable to adapt to changing circumstances?" Maybe it does, because the only way to establish & manage a eugenics program would be by establishing regulations strong enough to survive all challenges for hundreds of years-- a truly inflexible system.
...but let's assume that it doesn't. And further, let's establish the Spartan system farther back in history. Say, about a hundred years prior to the Trojan War, c. 1300 BC. Now the Spartan system has just enough time to get entrenched so that Sparta can displace Mycenae as the center of Greek civilization. Absent the vindictiveness of Agamemnon, the King of Sparta (who attacks Troy for economic reasons having nothing to do with the fair Helen) conquers the place & colonizes it (something that historical Sparta, for reasons of conservatism, never did-- but we're assuming that such extreme conservatism isn't a necessary feature of eugenics). Having conquered Troy, Sparta then proceeds to conquer the rest of Greece, the Balkans, the Aegean, & the nearer parts of Asia Minor. Again, something the historical Spartans never did, but there was nothing stopping them except their own inclinations.
At this point Sparta stops expanding & sets down to defend its empire while continuing to practice eugenics. Defending its empire requires an expansion of the army, which in turn requires an expansion of the citizen class (which is something the historical Spartans actually did, just once in their history, but never repeated). Adapting to changes in military tactics (because this Sparta isn't handicapped by extreme conservatism), & aided by the strength & fitness of its large professional army, it fights off the Persians, the Illyrians, & eventually even the Romans, preserving the integrity of its empire without further expansion. The urgent needs of defense are imprinted on Spartan society in a way that can never be eradicated.
Why no further expansion? Because the Spartans will have learned in assimilating the Greeks of their existing empire the difficulty of expanding the citizen class by getting non-Spartans to accept the Lycurgan Laws necessary to qualify them for membership in the army. Things like having their children examined, & if found unfit then exposed to die. Things like taking the children away from their parents at the age of 7 to be raised in barracks, to be soldiers. Because the Spartans would know that expanding the empire without expanding the army is suicide.
So the conquests of Alexander the Great never happen. The entire Hellenistic Period, with its virtual explosion of progressive innovation, never happens. Rome, when it finally rises, is cut off from the East, forced to expand into barbarian Europe, with a virtual wall separating it from Asia. So even if a city-state like Sparta can avoid extreme conservatism in its own polity, it still fosters by its very existence-- & by its ability to defend itself & to maintain its customs-- parochialism, conservatism, & anti-progressive tendencies in the world at large. Either that, or like any other culture it gets overrun & ceases to exist.
What form the Spartan Empire might take by the 21st Century is wide-open to imagination, but with its roots buried so deep in the past it would be likely to be a reactionary, imitative culture rather than a pro-active or inventive one. The needs of defense would dictate a culture with little art or culture as such. Slavery, helotry, or something very like it would likely persist-- unable to be changed by a world that was unable to conquer Sparta; & thus its production base would be formidable, but geared primarily towards the defense industries.