A buddy of mine climbed a high voltage pole one day when we were out longboarding. I forget how many feet it was, but if he fell even at 1/8 of the climb he would have died. He just moved some benches to get to the first rung and started climbing. He went to the top, and when he came back down he was soaking wet from sweat. I was actually kinda pissed he did it. The whole time I was thinking what was I gonna do if he fell.
Sounds like something I would have done 10 years ago. Fortunately I outgrew that phase. "WATCH THIS!"
Now that I think about it, would a chute even unpack quickly enough to save you. In base jumping you carry the chute in your hand. Seems like by the time you were going fast enough and had the chute out and inflated you would already be within seconds of splat. I guess you might, but you would have to act quick and know what you were doing, unless you like hanging by cords from a tower.
Your chute would come out plenty fast enough to keep you from hitting the ground at that height. Remember, the parachute is beginning its inflation at near zero fall speeds, not at terminal velocity. You're probably also going to carry something bigger than a 99 square foot gauze patch for a canopy. The biggest 2 obstacles in that base jump would be:
A: getting out away from the tower - there's no room to run to gain latteral momentum, you simply "jump" away.
B: the guide wires for the tower. If you can manage to make it 50 feet from the tower on your jump before your canopy inflates, you will only be 50 feet from guide wires to the left and right. If your canopy opens any other direction but forward, there's a lot of potential for bad things to happen.
Really though, when you think about it, it's not really that bad. I was just thinking of all of the tens of thousands of feet of ladders and scaffolding I have climbed over the years, some very unsafe and never had a slip or fall. What comes into play is nerves when you are over 1/4 mile off the ground.