I love train travel and advocate it whenever possible. However, it's not for everyone and it may not be the correct mode of transportation for your elderly parents.
Yes, you do have to haul your own luggage onto the train and store it in the appropriate places. Sometimes there are quick connections and long distances to walk to get to your correct car on the train. This is not a problem for many people - but it may be for your elderly father.
We were on the EuroStar from Rome to Florence and there were two elderly ladies attempting to haul their luggage up the train steps into their car. I stopped to help and they were quite ecstatic to have the assistance. Turns out they lived about an hour from me in Tennessee.
Maybe someone else would have stopped to help if I had not - but maybe not. By themselves, they would never have loaded/unloaded their own luggage.
Maybe there are porters for hire, but I never say one. Everyone carried and loaded their own bags.