Chris,
If you go by train look @ the lockers @ ZRH for your extra bags.
Tim et al,
Firstly, I did damage a car in this situation. I was young and took it, literally, off-road. One must take responsibility for ones actions. That, however, is no reason to not get a rental car in Switzerland. That can happen at home ;)
I am not disparaging Swiss rail travel when I suggest that someone get off the beaten path by renting a car. The Swiss transportation system is second to none, as I have said before, however there are some places it does not go, or at least, on my schedule.
There is a time and a place for every tool in my toolbox, car and train. Usually (read: almost always) a car is the tool I reach for. Sometimes it is because of my destination alone, but usually things like luggage security (security=peace of mind), ability to change my schedule and direction at any time (meetings and time schedules change), ability to buy and carry a meaningful amount of groceries due to having to cook a lot (celiac),
Sometimes the destinations demand it. Because many of the locations that I go to, if not more than 1/2 to 2/3 or higher, cannot be reached easily through the Swiss transportation infrastructure of rails & postbuses. I use places like Luzern and Grindelwald and Fiesch and some others as easy rest and (personal) refueling stations--nearby food, entertainment, and, yes, rail. But they are not my destinations these days. I end up in the Alp Krachtal at a queen bee mating station above Matt in Glarus or a parking lot below Capanna Corno Gries in the south repacking a little daypack so I and a small child can make the climb to the hut. I think these places are unique and beautiful and, without the right tool, a car, there is a large additional layer of...hassle...associated with getting there or there is no readily available rail(/or sometimes even postbus) option. In my case I found that a postbus that I needed only came by the tourist office at 8:30 every morning. The tourist office failed to mention that it only stopped if I made a reservation. They couldn't make it for me and the language was french (not my language). Maybe it is my fault for not knowing French/Romansch/Italian but, somehow, the car lets me circumvent these issues.
Keeping your stuff safe is an ever present worry while traveling for me. I my case we get our luggage from ZRH and head to the rental office. We get our car, pack it, and head back in to grab a few things: Coop/Migros groceries/water/sodas, a booster seat one year, a SIM card at SALT, maybe some ice cream before we leave for the little one, maybe hit the observation deck for 5 CHF (best bloody deal in Zurich), and sit down outside at the observation deck and look at our route on our iPhone. Then we get in the car and go. The whole time our luggage is safely packed away and we only carried an empty (then full) daypack to put our groceries and such in. I HATE to keep track of luggage (read: I hate having to worry about people robbing me...). I hate to think about first timers, over-packing because they don't realize what they can leave behind, and then having to keep up with that luggage the whole trip. I have been there in Luzern when our front desk guy had to tell a scream of four Japanese girls that they had walked about 4 miles to the WRONG hotel. He told them where their hotel was, back to the rail station and across town; they whined to each other and started off for about an 8 mile walk--with all of their overpacked bags (two or more each). I guess carrying all of that luggage around (two adults and a child) makes me feel like a never left the airport--HA!
Typically I don't drone on about the cons of rail travel so much as I try to talk about the pros of car travel. If I am there in winter it is perfect. We are planning an upcoming trip and plan to use rail for some or all of it. I like rail travel in Switzerland, I just like car travel more.