Is an electronic device an electronic device if it's turned off? Yes it is.
No, not quite. Take an American cellphone to Europe some time. It still looks like a cellphone, but you can't use it to make calls, and you can't even charge it since the sockets are different. As such it is no longer really a cellphone but just a bunch of plastic, metal, and wires. Same with an inactive tower. Its still a really tall building, or a volcano in Ur's case, but it doesn't do anything besides stand there. As such, its not a mythical, symbolic, powerful
tower but just a tower like any other. What defines it is its power, not its look.
Why would it be needed to stabilize Mundus? Nirn was created by Lorkhan, it was possibly even his realm before the Divine Pact. We've seen it's stable enough with only Adamantine functioning in TES IV. And wh would displacing the Heart deactivate the Tower? Displacing the Amulet never deactivated White Gold Tower.
It needs to stabilize Mundus because the Nu-Mantia intercept said so ( :rolleyes: ). Nirn was never fully Lorkhan's realm: he may have thought of it, but Magnus was its architect and uncountable et'Ada gave their lives to make it. Its his realm in a way, but its not as simple as a Daedric plane where the ruler is the realm. And again, you're not just moving the heart a couple miles away from the mountain (as you did with the Amulet), you're severing the enchantments that bind it to the tower and to the world. It literally goes *poof*
The Ayleids built White Gold Tower with an intention.
Yes, they did. And you expect me to believe that they had the way to achieve their ultimate goal and decided to not use it? "hm, we can try and become gods now, or we can admire the architecture for a few thousand years"
The crux of your argument is that the towers can be inactive. Show me one example where they clearly are (without the stone being destroyed) or one place that talks about them having to be activated.