When you've got as many tanks as me, yeah, the generator is a must. One or two tanks could probably be supported with battery-operated air pump filters and a fireplace to provide heat :P
CT power companies do trim ahead of time when branches/trees overhang lines or get in the way of maintenance. The thing is, it's a heavily forested state, and they can't cut down every single tree that could conceivably ever cross a power line. Nor can they trim trees on private property without the owner's consent (unless the town/state mandates the removal of the tree... did you know we actually have tree wardens?). See this summary for more info on state tree law
Given the size of trees, a trunk 40 or 50 feet away from the lines can fall and still take lines down - but it would cost billions of dollars (and get the environmental people up in arms, to boot) if the power crews were to remove every tree in a 50 foot radius of power lines. Removing all the trees is conceivable in prairie and desert states, where tree growth is sparse, but not so much so around here.