"height of prestige" is correct and usable in written English.
You can use it to refer to a point of high regard, respect, or admiration. For example, "The firm had achieved the height of prestige in the industry, earning glowing praise from its competitors."
One senior officer warned that his likely career alternative was the venal life of a businessman: "If you do business, you have to be dishonest". Rais would fall from the height of prestige--from the pride of defending Bangladesh, from those government cars and colonial club memberships and foreign educational courses, from that look people give an officer--to its depths.
As the narrator, the actor and singer Dorian Harewood, observes, it's the story of how one religion led Europe "out of the Dark Ages to unprecedented heights of prestige and power".
Brezhnev began brightly enough, with the Soviet Union at the height of its prestige.
At the height of his prestige, he has to be matched with a patsy on whom bookies' odds are sky-high.
Racine's withdrawal from the stage at the height of his prestige as a professional playwright probably sprang from a combination of factors.
The final part of the novel finds Shostakovich in the Brezhnev years, at the height of his prestige, being driven by a chauffeur like a paid member of the nomenklatura and confronting the costs of his own cowardice.
The famous mnemonic for this line, in the days when a classical education was at the height of its prestige, was: "Down in a deep dark dell sat an old cow munching a beanstalk".
Throughout western Europe, the dramatic arts attained new heights of cultural prestige, political importance, and commercial success.
Salvation's 'pain' today comes as hateful anonymous comments to posts; and ultimate suffering for sins comes in the form of public melt-downs, or precipitous falling from great heights of power, prestige and riches.
The President was at the height of his power & prestige here & in Europe.
