What stopped the West from seizing the Dark Tower remains?

[BalrogRingDestroyer]

I believe that the Ring's power somehow kept the tower itself up, as it was built in such an odd way that it was only held up by magic, so when the Ring was destroyed, it collapsed.

So while the Tower itself couldn't fall, why didn't the West at least ransack it to make it harder for Sauron to come back? Better yet, why didn't they take it over and turn it into the Light Tower or something? (Kind of the reverse of how Sauron turned Minas Ithal into Minas Morgul.) and build a built a ton of fortresses around it to further impede a return?

They seem to have put Minas Ithil near Mordor and even put a tower or so in it (which Sauron took over and "Sam the Elf Warrior" fought in.) But they didn't try and really do much further in. No taking over and fortifying the Black Gate, or at least filling it up with tons of rubble.))

 

[Ent]

How exactly would they have been able to "keep Sauron from returning"?
If not to where he did, why not Morgoth's old fortress in the North, Angmar?
Or why not a little farther east in the lands we know little about?
Or why not in good ole' Arnor, the former Northern Kingdom of the Dunedain?

This is kind of like after someone is murdered, or assaulted, or abused, etc., on the news we always hear well-meaning but completely "out of the loop" people say "We're going to take action and make sure this never happens again."

Really? There is no such ability existent among mankind even in the 'real world', much less in a mythology/fantasy work.

To give a 'humanistic' if speculative answer to the question, 'perhaps because they thought Sauron may well be no problem ever again, he being 'destroyed' and the ring being 'lost'." Man being predominantly lazy, why put in a lot of unnecessary effort? Added to that, perhaps it was the 'well, we'll get around to it someday' syndrome.

To put a theological/divine answer to it, it's because the Music has not yet reached its end, and in the providence of Eru there are other things to demonstrate with regard to rebellion and self-will yet, before all things are concluded.

Yet even at Sauron's end, we know Morgoth infused 'evil' into the very earth itself. And though Sauron is the latest (and last) physical "personification" of evil in bodily form, and is now gone, yet the evil survives. Future ages have yet to do their part until all things are brought to an end by the singing of the song aright.

And I'll stop there for now.

 

[Squint-eyed Southerner]

So while the Tower itself couldn't fall, why didn't the West at least ransack it to make it harder for Sauron to come back?

The Dark Tower was leveled to the ground, yet its foundations remained, and it was not forgotten.

Silmarillion, "Of the Rings of Power and the Third Age "

The "foundations" could not be destroyed as long as the Ring existed.

Better yet, why didn't they take it over and turn it into the Light Tower or something?

The same passage goes on:

The Numenoreans indeed set a guard upon the land of Mordor, but none dared dwell there because of the terror of the memory of Sauron, and because of the Mountain of Fire that stood nigh to Barad-dur; and the valley of Gorgoroth was filled with ash.

Not a pleasant place to live.

No taking over and fortifying the Black Gate, or at least filling it up with tons of rubble.))

They couldn't have filled it in, but they did fortify it; it was they who built the guard towers on either side, against the return of Sauron. These were later known as the Towers of the Teeth. I have a feeling they were likely called by other names when built, but if so, I haven't found them.

 

[mahalmar]

So while the Tower itself couldn't fall, why didn't the West at least ransack it to make it harder for Sauron to come back?

In The Silmarillion as @Squint-eyed Southerner pointed out, it is told that the Last Alliance leveled the Dark Tower to ground after the defeat of Sauron, and from the Tale of Years (Appendix B to the Lord of the Rings) it is obvious that the towers of Barad-dûr were in some sort of ruined state:

2951 Sauron declares himself openly and gathers power in Mordor. He begins the rebuilding of Barad-dûr. Gollum turns towards Mordor. Sauron sends three of the Nazgûl to reoccupy Dol Guldur.​

I believe that the Ring's power somehow kept the tower itself up, as it was built in such an odd way that it was only held up by magic, so when the Ring was destroyed, it collapsed.

That got me thinking... and write down some thoughts about the connection between Sauron and the Ring and Barad-dûr and Ainur magic.