In the book "The Master Of Mankind" this is actually expanded upon in a flashback with the Emperor and a Tech Priest of Mars. I can't find the actual quote, but even the Emperor concedes that they cannot be removed without killing Angron and he is of the opinion that an Angry Angron is better than no Angron

So it's a conversation with Arkhan Land

> 'Can you remove it?'

> 'Of course' the Emperor answered 
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> 'Then Divine One, why would you leave it there?'

> 'This is why'

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> 'They are the only thing keeping him alive' Arkhan said

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> 'A compromised Primarch is still a Primarch' The Emperor mused


It's split over 2 pages so I've trimmed some none relevant pieces