Of course, the train trip will be longer so, tradeoffs.
If you count everything in, a high speed train is faster or close enough (but compensating with much higher levels of comfort and most of the time being spent in the train itself, not separated in travel to airport, queuing there, wasting time there, boarding, flying, disembarking, waiting for luggage, travel from airport) with air travel less than 3 hours.
Last August I travelled from Paris to Innsbruck by train with my 6 year-old daughter. Despite a misconnect in Germany after a delay to our TGV and then a cancelled ICE causing us over an hour's delay (although that was an excuse for a surprisingly good impromptu stir-fry for lunch at Mannheim station), then subsequently having to run, with five separate items of luggage, none of which she was carrying :) to connect in Munich, we had a great day.
I did an almost identical trip by car with my eldest years ago when he was also 6, the only things I remember about it were watching sun rise over Paris as we left, and sun set over Munich as we drove round on it on the Autobahn. The rest was just hours of keeping my eyes on the road.
Given the choice, I'd take the train every time.
When my spouse and I did a 3-week vacation in Europe and then a 2-week vacation in Japan, my one steadfast condition was that we were allowed one 19-liter backpack and one 23-liter backpack, full stop. If it didn't pack into one of the backpacks' zippered pouches, we didn't take it with us. It takes some planning and hacking to do well, including optimizing clothing, toiletries, and electronics for traveling with that little space, but the handful of times we had to get from point A to point B quickly through a crowd, it was glorious.
It's also nice knowing that all of my luggage trivially fits under the seat on the airplane. Takes away any stress relating to "OMG will there be enough overhead space?" panic that everyone goes through when jockying for a spot in line to board. I try to be the very last person on the plane, because I don't ever see the point of being in a hurry to squeeze myself into that tube before I absolutely have to.
It turned out we didn't miss the luggage we couldn't fit in the backpacks at all. The last time the family went to Hawaii and then to San Diego, it was the same story. One 19L backpack for me and each of the kids and a 23L backpack for the spouse. Again, no problem at all and totally worth it.
I couldn't help but think, "Heh, amateur!" when I read about the OP needing a grotesque 45L of luggage for a few days of travel mostly just sitting on a train. I guess I'm officially now one of those ultralight traveling snobs. If I'm not debating whether I really need 5 pairs of nylon underwear or if I could get by with 4 or maybe 3, I'm feeling like I'm not putting in enough mental effort in preparing for the trip.
