Thats not always the case, like when Karin or Ays arm were burning.
Bee was being burned by flame A. Karin was touched by flame A. So why is Karin being burned by flame B?
Susanoo was burning with flame A. Ei hit flame A. So why is he burning with flame B?
If Karin and Ei were hit by Flame A, should they not had been burned with the power of flame A?
Also note that neither Bee nor Susanoo were instantly burned despite being focused on.
Its obvious for anyone who pays attention. Itachi burned through frogs stomach in second, but when he was out of picture the black flames wered enlarging the hole at all.
Sasuke's Great Dragon Fire put a hole through a roof, but didn't do much damage to Itachi's arm. Should it had not blown off Itachi's arm too?
Great Dragon Fire was also hot enough to help heat the sky and make stormclouds, shouldn't it had done more burn damage to Itachi's arm?
It's called plot. Everything is as effective as the plot demands. Itachi needed a way out of the frog stomach.
Amaterasu works by focusing your vision on something.
Amaterasu is Amaterasu.
Hmm i came in here to say it isn't. But you make a good point so maybe Itachi has more power in his and Sasuke simply has better control. Because his eyes abilities are literally Amaterasu and Enton which gives him far more control over Amaterasu than the solo god.
Your initial assertation was correct. This is all fanon to explain it's inconsistencies and to disregard anything that isn't complementing.
Fanon Amaterasu has more mechanics than canon Amaterasu.