Other than the AVX side channel, the interesting thing is that it demonstrates that the remote aspect definitely works. Before, it was theorized but might have proven to never give sufficient signal. While many were confident, now we know.

Further, it shows how to do it (classifier) and gives a very good model for what bandwidth can be expected in practice. And still further, that bandwidth is entirely sufficient for attacking long lived cryptographic key material. Before, it was easy to theorize that the bandwidth would simply be too low. Now it isn't.

This is also really good because the bandwidth is really low. For data larger than a key (or where you would need to scan a lot to find the data), we can be much more comfortable with infeasibility arguments by basing them on some security margin beyond these experiments. As an example, if it would take 1 <timeunit> to exfiltrate a single credit card number even if the technique got 10 times better, maybe that means it isn't a sufficient risk. Or maybe it is. (All depends on the time unit and the risk.) But now we can make that assessment with a real baseline instead of a guess.