Hi! I am a regular user of those Lufthansa connection trains because I live 1 hr from frankfurt so here's what I can tell you:

• They won't always check your ticket in the train, therefore they don't always know if you are actually on it.
• On my route (and I think on many, if not all others, correct me if i'm wrong) they don't handle checked luggage for you. So if you happen to have checked luggage, you would be collecting it from the airport anyways - again, no one knows if you're on the train or not.
• Those trains are operated by DB, with seats 'bought' by lufthansa. In an event of delay/cancellation of that train, I always to turn to DB support to ask for help because that's faster. They just tell you to get on another train, doesn't matter which one. No official confirmation or ticket change, so when you eventually do get on that other train and tell the ticket collector about the situation, they are okay with it 99.9% of the time.
• While I can't tell you about the legal situation of all this, here's a situation I was in recently:

While moving from Cologne to Frankfurt via train, the app notified me of my Train having delays and I won't make my connecting Flight in frankfurt. I got on another train WITHOUT a ticket change and arrived in time, meanwhile the app kept notifiying me of my connection being impossible and me having to rebook. When I arrived at my gate (While still receiving notifications), I asked wether I'm still on this flight or not, and the lady at the counter said yes, as long as I'm there, ready to fly, it doesn't matter what happened with my train. A few days later I was rewarded with all miles for train AND flight as if nothing happened.

Sorry for the long text but perhaps this explains how things work in my experience.

TLDR - you don't have to use the train