You could say in a way, Earth is the natural enemy to the TSAB who want to use magic for clean energy. The fact that most Earthling don't have the ability to use magic, made that basely a useless way to power things for Earth. So Earth had to turn to other places to run there power. Even if that meet energy sources that would lead to the making of Mass-Based Weapons.
You can say that the TSAB wouldn't try to force Earth to become an administrated World unless Earth does something too major but there a high chance that as Earth continue to made Mass-Based Weapons, the TSAB would get more and more afraid of them becoming a threat to the fact that they are the current superpower of the multiverse.
The fact is that if Earth found away to travel between dimension like them, they would become very hostile to Earth. As Earth's tech get better and better, in 100 year from now in the timeline Earth would most likely be look at as something that the TSAB would want to destroy.
This isn't even going into as the leadership of the TSAB change there a higher chance a very evil person would end of getting into control and try to just enslave everything. Basely a rerun of the event of Belka/Saint War happening when they try to force everything under there control.
You can even say that the TSAB is a Military run state and the Military have control over all government stuff.
The biggest reason that the TSAB is very deadly and bad for the Multverse is because they don't have a rival or another superpower to kept them in check somewhat. They have free control to do whatever they want.