#Dyalog APL, 14 bytes
Dyalog APL, 14 bytes
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(?351)⊃⎕A/⍨⍳26
Gives instant results. Works by selecting an evenly distributed random character among "ABBCCCDDDD..."
(?351)
RandInt(1,351)
⊃
picks among
⎕A
"ABC...Z"
/⍨
element-by-element replicated
⍳26
{1, 2, 3, ..., 26} times