It's not difficult to call Afghanistan NATO's greatest defeat when the three other wars were all victories. The U.S managed to remain fit for leadership after the categorically bigger defeat it faced in Vietnam. It doesn't follow that despite having a larger and more advanced military than ever, 22,000 casualties in a counter-insurgency over a 20 year period voids it's ability to protect it's allies.
Not certain what you mean by "turbulent last four years" in NATO. If by that you mean the Trump presidency, then your final recommendation for Europe to look to it's own defence basically aligns itself with his policy towards NATO.
Should have said 'the West' instead of NATO, my bad.
The problem I see is not a military one; it would be a damn shame if even with this needlessly big military budget the United States wouldn't be capable of executing large military operations. No, it is much more one of political will to take over the leadership of the West and not just think 'America first'. The hasty and uncommunicative retreat out of Afghanistan is just another example of that apparently lacking.
By 'transatlantic alliance' I mean the traditionally close partnership between European countries and the US, not just NATO. The Trump presidency and it's continuous attacks have left a bitter taste for most Europeans. Even though Biden is trying his best to act like nothing has happened, these wounds will need time to heal. Though, will they have the sufficent time to? What if after the current chaos Trump gets another 4 years? Or another politican with similar views on foreign affairs?
I am by no means proposing for Europe to cut all it's ties with the United States - a proposal most unrealistic with nothing to gain from neither sides anyway - but the current events in addition to the experiences made by Europe the past years should lead to them being more pro-active and independent, since you simply cannot fully rely on the United States anymore.