My understanding of the result that was found is that the blowup doesn't happen in the real world, and only happens in an NS simulation. The bottom line is that NS is insufficient to model the real world, because in this case the real world is more stable than the model. [Take this with a grain of salt, I barely knew of NS before a couple days ago]
I'm not too familiar with the exact problem as I only became aware of it due to this drama, but I think you're correct. That said, another commenter noted that it may also be one of the Millennium Problems with the least application. We already know "all models are wrong, but some models are useful" (George E. P. Box), the fact that this holds for Navier-Stokes is not a surprise.
To my understanding, the problem was never about the real world really. Navier Stokes approximates a fluid (which is made of discrete particles) as a continuous volume. The point of showing that you can achieve unbounded increase in velocities is that the approximation breaks down - it's a clearly an outcome that can't happen in the physical world.