Why? Well, I have jotted below my own reasons for making sure the tripod always comes with me on trips like this. They are all pretty well 'kicking myself for not bringing it' reasons too.
1. Compositional Aid - the tripod slows me down. It stops me being too impulsive and simply pointing and shooting at a scene I think might work, and then moving on. There can be a temptation to secure as many 'good' landscapes as possible when out on a shoot, and this involves rushing around, looking at everything and yet seeing nothing.
So how does the tripod slow me down? By the time I have taken the tripod out of the bag, extended the legs and put it up where I think it can do most use my whole tempo has slowed and is starting to guide me to scenes that might work well. I am now becoming more in tune with what's around me.
Also, I can shoot at differing heights, angles and directions - and the fact that I have now secured the camera to the tripod allows me this facility more readily. I am NOT rushing, and am considering more carefully what looks good, and what looks better.