I have seen that even when TAN crosses TBN, it's not an assurance of immediate demise of the fluid nor equipment.
Most folks don't understand why we use TBN/TAN. It's a tool to use as a predictor. It does NOT indicate wear; it is only a predictor that cautions one to pay closer attention to the lube condition.
For example, if you were running long OCIs with a syn/BP filter, and did a UOA every 5k miles, you would want to track TBN/TAN. At some point, TAN will cross over TBN. At that point, depending upon the range and "velocity" of the shift, you may want to start doing UOA with greater frequency, to look for an escalation of wear particles indicating the fluid has become corrosive. Often, the size of the sump will dictate how the fiscal decision plays out; cost of the OCI vs. cost of UOAs.
We use lubes to reduce wear; that is THE MAIN GOAL of lubicants. Inputs such as vis, FP, TBN/TAN, are all predictors of the potential lifecycle of the fluid. But wear data is the actual result of how it truly performs.
I've seen TBN be usurped by TAN in many of my longer OCIs, and never was the wear rate affected adversely. That is because, although I ran an extended OCI, I didn't extend it far enough to allow the relationship to become adverse.
Cross over is a mile-marker to pay closer attention; it should not be thought of as an automatic trigger to dump a fluid.
OCIs based upon the odometer are the least-common-denominator approach to lube program maintenance. They are simple to follow; they are reliable and provide for a safe operating condition. But they are wasteful. Extended OCIs with UOAs, PCs and other indicators are a way to manage the OCI to a good fiscal end. And using TBN/TAN is a way to further refine that approach to a greater level of detail. But it also ups the cost yet again. UOAs are tools, not toys (although one would be often hard pressed to recognize the difference on this site). Knowing how and why to do a UOA, and what to do with the data afterwards, is the real challenge.
I have yet to see a UOA posted here that showed a direct correlation to wear and TBN/TAN crossover. And my own personal experiences have shown this to be a non-issue for "normal" applications, to the point where I'm no longer paying for the TBN/TAN testing for any UOA at less than 15k miles. Even if it does "cross over", it does not manifest into a wear issue in short-to-moderate durations.