Sparta was good at fighting, but bad at war!
Spartans were known to have terrible logistics, they couldn't field an army for more than a year. Back then, most armies needed to live off the fat of the land and/or have huge supply trains to remain effective, and Spartans had neither skillset. (When talking Bronze age tactics: this was the key advantage of slingers, who could craft their sling-bullets from clay and rocks found near the battle areas. Mass production and distribution of arrows was still not mastered in the 1000 BC-era or so)
As such, Spartans would "gloriously" run into a few battles, declare themselves superior, then go home. While the enemies would just keep marching towards their target, sustainably pressing forward.
Its like watching an expert Sprinter battle a Marathon Runner. War is a marathon, not a sprint. Consider the Persian armies that fought against the Greeks: thousands of miles away from home.
In contrast, Spartans fought on their home turf and barely were able to do so effectively. Sure, they won a lot of battles, but holding back the Persian army required more than just winning a battle here or there.
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That's why the Athenians worshiped Athena: the goddess of wisdom _and_ war. They realized that waging war was both an issue of might and intelligence. Intelligence to move your supplies and organize them so that your armies can stay in the field longer than your enemies.
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That being said: the Marine Corps glorify the Spartan way of thinking, because the USA's Marine Corps are designed to be the spearhead of battle.
The Army is more about logistics. Its got less glory but is more practical. They don't glorify the Spartan way.