Have you read the treaty? I've gone back and skimmed it. My initial recollection is reinforced: most articles don't mention the US at all, and those that do are chiefly concerned with its function as a depository.
Of course I have, and long before this discussion. If you aren’t grasping the way those articles make the U.S. central to the function of NATO through its role in the administration of the treaty, I don’t know what to tell you. A NATO that had to deposit any accessions or renunciations with the government of a renounced member would be an absurdity. And a U.S. that withdrew from the treaty would have no treaty obligation or right to accept them.
It's a treaty, not a constitution. It doesn't need an amending formula. The non-US members could meet, agree to adopt the provisions of the treaty with the replacement of the US by some other depository state, retain all the other trappings of the organization and start unwinding US involvement, and be done with it. Preserving NATO without upending everything just because of some rules lawyer quibbling isn't some concept that people should have difficulty wrapping their heads around.
[Add: "With regard to security rather than trade, we already have NATO, which could be adapted in whatever respects necessary if the US decided to make a full exit" doesn't mean the original treaty needs to be preserved as an artifact.]
A treaty without an amending provision can be replaced with another treaty, but not changed in part but otherwise retained in its current operation. What you describe is a replacement treaty, as I said. If you want to imagine all of NATO minus the U.S. simply agreeing to a new NATO that’s otherwise the same, then I respectfully suggest you’re wilfully blind to the defence and security dynamics - including U.S. predominance - that made NATO in its current form attractive in the first place,
and are just skipping past and ignoring other tensions within the alliance.
Absolutely European and other allies could negotiate a new defence pact, with or without a mutual defence ‘trigger’ along the lines of article 5. Much infrastructure, policy, and bureaucracy could conceivably pivot to serving this new alliance. But make no mistake, it would have to be reassembled into a new framework, and that would not be quick, easy, or seamless, nor would it be NATO. It would be something new.
Realistically I struggle to imagine all or most of the current NATO partners would, faced with NATO as it stands dissolving, commit themselves to the same sort of obligatory mutual defence that was attractive in 1949 staring across the top of the Iron Curtain at the prospect of nuclear oblivion. Nor can I imagine many current NATO members wanting to enter a new arrangement hamstrung by the sort of unilateral veto with which figures like Orban could hamstring the alliance
NATO continues today in its present form largely out of inertia and because, tensions notwithstanding, it’s still attractive to retain for a host of reasons because it’s already set up and running. But a U.S. renunciation would force the creation of a new arrangement, and in that rebuild of a new security architecture we would see a lot of things done differently.