Ok after reading all of this, DDM and co. are almost on the money when it comes to the Emeralds' power. Sure they're "inconsistent", but not really. It's a "Yes, but actually no" type of deal. I'll explain.
inhales deep
The Chaos Emeralds house infinite power. It's been stated in SA1, Sonic Battle, Shadow the Hedgehog, and many other games before and after it. The Emeralds can really be just as powerful as they want (as they were created by unknown Gods based on some Classic Era scans), but can be as weak as they want. Why? Because it depends on the user who wields them!
"The servers are the 7 Chaos. Chaos is power... Power enriched by the heart. The controller is the one that unifies the chaos." -Tikal
Tikal states that power is enriched by the heart. The heart is mostly a metaphor defining feelings and emotions. And the user who has the most positive emotions, or in this
aptitude, has more control or power with the Emeralds. Hence why Blaze stated that the Emerald's can turn your thoughts into power. Which explains why Super Sonic has beaten Perfect Chaos in SA1. Or in Sonic Rush, Blaze lacked the positive emotions to bring back the warm and glowing energy of the Sol Emeralds until Sonic and co. help
bring back the glow from the Emeralds. They were like ordinary stones, but became normal because of the "Power of Friendship", literally (which we all know are just parallel versions of the Emeralds so this analogy makes sense).
So we got the whole positive emotions part out of the way, but what about aptitude and variable AP? It's because with that aptitude the Emeralds HAVE a variable tier in power. It's why the Emeralds can destroy planets in one game, pierce stars in the next, a freakin' city, an entire universe and multiverse, then back to planet level just like that. It's because various characters, when using the emeralds, responds differently. Here are some examples:
>Shadow almost dying from using them in his Super Form after his sudden change into the good side
>Chaos going malevolent in his Perfect Chaos form where he destroyed the Echidna Tribe and almost wiped out an entire city
>Ix getting one shot by Super Sonic even though both use the same source of power
>Emerl going haywire and died mostly after absorbing all those Chaos Emeralds
>Tails going super with the Super Emeralds, but not with the Chaos Emeralds unlike Sonic and Knuckles And that's all I got for now as far as examples go.
So DDM, Cal, and anyone else who's in this downgrade, this is why the Emeralds have been showing different forms of AP in different games. It's not because of inconsistency, it's because of the aptitude of the ones wielding the emeralds. Or machines who are specialized to use a set variable because science.
Here are more sources that you
need to look at:
https://sonic.fandom.com/wiki/Chaos_Emerald
https://sonic.fandom.com/wiki/Master_Emerald
https://sonic.fandom.com/wiki/Chaos_Control
https://sonic.fandom.com/wiki/Tikal