My 68 used to be my daily driver. I used it as a DD for about 1 year, before the accident which took it off the road and motivated me to completly redo it. Anyway while it was my DD it saw about 10 road trips all of which were over 300 miles one way. I never had a problem with the car and it never left me stranded. The only thing I didn't like was the vinal seats in the summer time, with no a/c.
If you keep the car well maintained, and upgrade a few things like electronic ignition and a newer carb then the chances of it leaving you stranded are about the same as with a new car.
I do suggest that if you do make this your DD to upgrade your seat belts from a lap belt to a 3 point harness. (I learned that the hard way when my face ate the steering wheel in my 68, during my accident.) Also upgrade the brakes, to at least front disc if not 4 way disk, power assist.
As Pakrat said, the chances of your baby being in a accident are proportional to how much you dirve it.
So if you are OK with the chance that the car may get totaled, and the car is in good running order, then by all means use it as a DD.
Mario