A train that doesn't arrive at all is also not considered late.

I have this same argument with my spouse. If fifteen minutes late is "on time", then change the arrival time and just be on time.

Luckily the next train you have to take is also late, so nothing really changes. A system so broken that it works "perfectly".

I'm not sure I agree. The real world is never going to run perfectly, so some slack must be included (either by adding buffer time to schedules, or using the way you mention). Of course there are examples like Japan that have done a really good job at optimizing these systems, but you won't be able to successfully apply their approach to every country. Some locations require more work to achieve this, others require less.

Generally the closer you get to an "ideal" performance, the more costly every further improvement gets. If 7 min isn't reasonable, what number would be? Say we manage to shave off two minutes, at twice the cost of the current system. Is that really worth it?

The better approach is to include reasonable slack time in people's train schedules, while increasing frequencies so missing a connection doesn't result in hour-long wait times.

Having been on a delayed German train, my connection actually waited so that everyone on my train connecting to it could catch it...