ICE test train reaches speeds of up to 405.0 km/h

I fear that the general public in Germany will not be praising this achievement. The once efficient and punctional trains in Germany have deteriorated severely in the past years due to lots of delayed maintenance causing lots of delays and even regular cancelations of trains. Also the road infrastructure is suffering from delayed maintenance.

That's exactly it, it's not the new top speed they need, they lack efficiency. And it's not just Deutschebahn. For example BVG, who runs busses and U-bahn in Berlin is even less reliable.

I think higher speeds can help efficiency. For example it can help catch up a train that has been delayed.

West European rail is very full, so rail use is carefully coordinated, since trains of vastly different speeds (e.g. ICE vs a regional train) use the same tracks.

If an ICE is, say, 15 minutes late, they cannot just drive faster to catch up. The schedule went on, and at that point there may be a much slower regional or intercity train on the same trajectory.

This is why ICE delays tend to cascade. It starts with a short delay, the ICE gets stuck behind a slower train, increasing the delay, etc.

The solution is better maintenance of tracks and trains, adding more rail capacity, adding redundancy, etc.

Of course, these are all much more expensive than an ICE speed experiment for PR.

If it is the same as in Switzerland, the solution is in helping people get the health care they need. Most time I got annoying delays when I was living in Switzerland was because of a "personal accident" which 99% of the time meant someone had deliberately jumped in front of a train.