According to the article, Norman influence led to double letters being used to better mark out sounds, which achieves the same as diacritics. It made English mostly good enough (failures like 'lead' are rare). Being good enough, and lacking a strong central authority, the language only accepted a conservative standardisation, and avoided larger changes such as including diacritics. Without these Norman changes, there is more chance diacritics would have been added, as it would not have been 'good enough'.
Written English is a worse is better story. The Norman influenced version being the first-mover that users cling to even when better comes along.
Well, the "lead issue" could be fixed by writing the verb "leed" (after all, it's exactly the same sound as in the word "queen" mentioned in the article), but for some reason this hasn't happened...
It happened in newspaper jargon for the leading sentence of an article (though they used the spelling "lede" instead), because "lead" was already a metonym for hot type (which was cast out of the metal).
It hasn't happened otherwise presumably because the risk of confusion is normally very low when not in a Pb-filled context.
Diacritics wouldn't have helped moderns if they were in from the beginning - most of the confusing words used to be pronounced like they are spelled (at least to people of the time). Maybe they would have helped to petrify pronunciations and slowed or stopped linguistic drift but I somewhat doubt that given historical literacy rates.
But is that why they avoid diacritics? It sounds like English probably wouldn't have had diacritics even if the Normans hadn't come in.
Seeing my son try to learn to read things like "cycle", I feel like diacritics would make English writing a lot more accessible.