Cotter Pyke é o único analfabeto entre os altos escalões?

TL; DR: Os que mencionamos na minha resposta são:

• Davos Seaworth
• Bronn
• Amory Lorch
• Dunk

No entanto, é provável que a maioria das pessoas de baixa renda que chegam a uma posição mais alta na vida adulta seja provavelmente analfabeta.

Quanto aos membros da Patrulha da Noite, não pude encontrar nenhum caso explícito, mas não seria surpreendente saber se eles tiveram um membro analfabeto nos escalões mais elevados.

"You do it. They have parchment and ink at the Citadel, as well as longbows. I will expect you to continue with your practice. Sam, the Night's Watch has hundreds of men who can loose an arrow, but only a handful who can read or write. I need you to become my new maester."
_{A Dance with Dragons, Jon II}

Se considerarmos os First Rangers e os Wandering Crows como superiores / comandantes na Patrulha da Noite, provavelmente houve alguns poucos que eram analfabetos. Assumindo com os nomes conhecidos que se alguém tem um sobrenome, e então uma casa, eles provavelmente tiveram o ensinamento de um Meistre, então nós não conhecemos a Primeira Guarda Restrita iletrada, mas nós temos alguns Corvos Vagueantes que não têm Casa: Conwy, Dareon, Gueren e Yoren .

Abrindo isto para qualquer Senhor, temos o caso do Senhor Davos Seaworth que não sabia ler nem escrever.

Obediently, he selected a paper at random. "It looks handsome enough, Your Grace, but I fear I cannot read the words." Davos could decipher maps and charts as well as any, but letters and other writings were beyond his powers. But my Devan has learned his letters, and young Steffon and Stannis as well.
_{A Clash of Kings, Davos I}

"I am lowborn," Davos reminded him. "An upjumped smuggler. Your lords will never obey me."
"Then we will make new lords."
"But... I cannot read... nor write..."
_{A Storm of Swords, Davos IV}

Bronn grinned. "My knightly sigil. A flaming chain, green, on a smoke-grey field. By your lord father's command, I'm Ser Bronn of the Blackwater now, Imp. See you don't forget it."
_{A Storm of Swords, Tyrion I}

"Bronn put a dagger in his eye, and told me I had best be gone from Stokeworth before the sun went down or I'd get the same. He said he'd pass me around to the g-g-garrison, if any of them would have me. When I ordered Bronn seized, one of his knights had the insolence to say that I should do as Lord Stokeworth said. He called him Lord Stokeworth!" Lady Falyse clutched at the queen's hand. "Your Grace must give me knights. A hundred knights! And crossbowmen, to take my castle back. Stokeworth is mine! They would not even permit me to gather up my clothes! Bronn said they were his wife's clothes now, all my s-silks and velvets."
_{A Feast for Crows, Cersei VII}

Na verdade, é explicitamente declarado por Tyrion que Bronn não sabia ler.

That night, when the Red Keep was dark, Bronn arrived to find him sealing a letter. "Take this to Ser Jacelyn Bywater." The dwarf dribbled hot golden wax down onto the parchment.
"What does it say?" Bronn could not read, so he asked impudent questions.
_{A Clash of Kings, Tyrion X}

No programa também temos Sor Amory Lorch, que acidentalmente enviou uma carta a House Dormand, em vez de House Marbrand, porque ele não sabia ler.

Tywin Lannister: Can you read? My lord? Can you read? This letter detailing our infantry movements was meant for Lord Damon of House Marbrand. It was sent to Lord Marlyn of House Dormand.
Armory Lorch: My apologies, my lord.
_{Game of Thrones, Season 2 Episode 6, "The Old Gods and the New"}

Como @DariM aponta mais tarde no mesmo episódio, Tywin diz a Arya que Jaime está lutando para ler e então Tywin o ensinou pessoalmente. Também parece que Jaime é disléxico.

Tywin Lannister: Who taught you to read?
Arya Stark: My father, my lord.
Tywin Lannister: Hmm. I taught my son Jaime to read. The maester came to me one day, told me he wasn't learning. He couldn't make sense of the letters. He reversed them in his head. The maester said he'd heard tell of this affliction and that we simply must accept it. Ha! After that, I sat Jaime down for four hours every day until he learned. He hated me for it, for a time. For a long time. But he learned.
_ibid

A partir disso, podemos inferir que baixo ou alto nascido em Westeros nem todos poderão ler, mesmo que tenham acesso aos ensinamentos de um meistre. Jaime só pode ler agora porque Tywin não desistiu quando os meistres já o fizeram.

Nas histórias de Dunk e Egg, também aprendemos que Dunk, mais tarde Lord Commander of the Kingsguard, é analfabeto.

The old man had ridden with some of these knights; others Dunk knew from tales told in common rooms and round campfires. Though he had never learned the magic of reading or writing, the old man had been relentless when it came to teaching him heraldry, often drilling him as they rode.
_{The Hedge Knight}

Dunk the lunk, thick as a castle wall. He felt his cheeks reddening again. Gingerly he took the parchment from the maester and scowled at the writing. Not a word of it was intelligible to him, but he knew the wax seal beneath the ornate signature; the three-headed dragon of House Targaryen. The king's seal. He was looking at a royal decree of some sort. Dunk moved his head from side to side so they would think that he was reading. "There's a word here I can't make out," he muttered, after a moment. "Egg, come have a look, you have sharper eyes than me."
_{The Sworn Sword}

Nossos estimados membros já mencionaram os caracteres analfabetos de pessoas de baixa renda ou recém-nobres.

Aquele Senhor era Borros Baratheon , neto de Lady Alyssa Velaryon que era mãe do rei Jaehaerys I Targaryen dela primeiro casamento. Por isso, é curioso que uma pessoa descendente das mais altas e nobres casas do reino (Baratheon, Durrandon, Velaryon, Targaryen) nunca tenha aprendido a ler e a escrever.

Yet all the witnesses agree on what Lord Borros said and did. Never a man of letters, he handed the queen’s letter to his maester, who cracked the seal and whispered the message into his lordship’s ear. A frown stole across Lord Borros’s face.
_{The Princess and the Queen}

Bem, o mais famoso é provavelmente Sor Davos Seaworth.
Há várias cenas / passagens descrevendo-o aprendendo suas letras (para ler). Significa que ele não sabia ler no começo do primeiro livro / temporada.

Claro, isso está relacionado a como ele ganhou sua classificação.

Eu não ficaria surpreso se Sor Bronn, da Blackwater, fosse analfabeto, exatamente pelas mesmas razões.

Aparentemente, não é tão incomum. Podemos dizer isso a partir do seguinte monólogo de Lady Dustin sobre os maestros:

If I were queen, the first thing I would do would be to kill all those grey rats. They scurry everywhere, living on the leavings of the lords, chittering to one another, whispering in the ears of their masters. But who are the masters and who are the servants, truly? Every great lord has his maester, every lesser lord aspires to one. If you do not have a maester, it is taken to mean that you are of little consequence. The grey rats read and write our letters, even for such lords as cannot read themselves, and who can say for a certainty that they are not twisting the words for their own ends? What good are they, I ask you?

_{A Dance with Dragons, The Prince of Winterfell}