I wish people would distinguish what they mean when they say:
The
Satellite; which alone refers to the bronze age/Satellite Era orbiting Satellite. Round shape.
The
Watchtower; which refers to the Morrison era, Moon-base tower.
And the
Satellite-Watchtower, which refers to the more modern hybrid of the two. Meaning the Orbiting Satellite in the shape of a Tower.
But if you just say Satellite, I'm assuming you mean Bronze age one.
And if you just say Watchtower, I'm assuming you mean the moon-base.
As to the Hall of Justice, whose location is not hidden (see the Sanctuary for that), and not out of reach, but intentionally in public, in
the middle of a City.
As per it's intro above, and re-intro, it's a fine idea as intended, it should only ever be a general meeting place, and house teleporters to the Satellite-Watchtower. And be the
safe public face and presence of the heroes on Earth.
That's what it's for.
It should not contain "the most powerful and dangerous objects in the multiverse". LOL!