No, Henry. Modern multi-coatings increase light transmission. That is one main purpose they are designed for. Period.
You should compare a modern coated lens with an old uncoated lens, and then you will see that the modern lens offers better shadow detail.
If all the improved coating technologies of the last decades would have resulted in less shadow detail as you claim, lens designers would definitely not have used them.
And as already explained, I have lots of these different lens types with different coatings. I have the evidence in my work here.
Best regards,
Henning