Picture a narrow lane running between two buildings. Standing at the mouth of it you cannot tell anything is wrong; it looks exactly like the lanes that go through. So you walk in, and you keep walking, and at the far end there is a wall. The word lives in that moment at the wall, and not in the wall itself. What it really carries is the distance you covered while believing there was a way out.
From the word’s history
Wiktionary explains the blind in this phrase as the lack of a through passage: the way out was thought of as the alley's eye, so an alley with no way out is blind. The phrase is attested from 1583, and has been used figuratively since the middle of the 19th century.
Wiktionary 說明這裡的 blind 指的是「沒有通道」：舊時把出口想成巷子的「眼睛」，沒有出口就等於看不見。這個詞從一五八三年開始有紀錄，到十九世紀中期才被拿來比喻。
Wiktionary, entry blind alley (packet source_ref kaikki:3f6f69a190036ae4:1581717468)
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