Not all railway companies participate in AJC. E.g. neither Snälltåget operating the Stockholm - Berlin night train and nor Flixtrain offering budget tickets between Berlin and some German cities are participating.
So don't use the open access competitors for complicated trips with multiple tickets. There always are traditional alternatives, especially now when the Swedish government and SJ started running their own daily Berlin service.
I love Italo, Snälltåget etc. but it's best to use them for a well-contained itinerary.
Additionally to AJC rights typically the traveller's insurance covers reaching destinations in case of train delays. It's not as grim as the grandparent makes it sound.
At least my insurance has a list of causes when they pay. Besides that the list does not cover all (e.g. in Germany a common cause to cancel train these days is because of lack of staff, but my insurance does not list such cause) it's generally impossible to indentify the cause. There are network effects. Train A breaks down, train B cannot pass, train C should be taken over by staff arriving on train B. So what is the reason that train C runs late or gets cancelled?
In Finland the causes for delays can easily be read from an open data API. Having looked at it, it is completely ridiculous: The conductors seems just to enter some more or less random code at every station.
I doubt any insurance will pay for any kind of missed connection, no matter what.
Costs of alternative transport and accommodation due to missing a connection within public transport is covered in my insurance, unless the reason is a strike, bankruptcy or negligence of the passenger. And only if the connection is not the transport operator's responsibility.
As an example in their marketing material, they use a public bus breaking down on way to the airport.
I haven't used this coverage but I think it shows that there are insurance policies to cover missed passenger-designed connections.
Interestingly enough the EU thinks that strike is the responsibility of the company, they have to pay the compensation according to passenger rights (even after the rights have been reduced in the recent reform).
My insurance, too, does not pay in case of strike. Strike is seen as force majeure in many contracts.
I would agree with the EU. Employers have the bigger power on the labor market, it's their responsibility to keep working conditions good enough to avoid strikes.
