So I know it effects it because I’ve experienced it but you need me to prove it.
The easy answer would be to tell you to google it, as several others have explained the “why” you’re seeking.
Excessive drive pressure defeats the scavenging effects of valve overlap this hurting the engines efficiency, which requires more boost to accomplish the same power and thus higher EGT.
Hopefully that makes sense, and I’m once again able to pick engineers out of a crowd retaining my 100% accuracy rating on that.
A decent explanation will suffice, you don't need to prove it, but a little more than saying "believe me" is helpful.
To the point you make here, I don't disagree except with the logic in saying "which requires more boost to accomplish the same power." The exhaust pressure increase isn't causing IAT to increase, it's causing a drop in VE, that leads to a power drop, and then a decision is made to increase boost pressure to try and regain the lost power. The exhaust pressure isn't causing the IAT to rise.