We put our trust in someone else's calculations and measurements all the time. It's just part of the modern world. Cross a bridge, drive a car, use anything electrical, and we implicity trust that the people who designed it, built it, installed it and tested it have done their job correctly. Occasionally things go wrong and disaster strikes, but, by and large, the things we make use of in our lives work properly.
That said, do you fancy trusting the people who designed and installed the ladder up the Gloucester Tree, at Pemberton?
This was originally built as a fire lookout, amongst the majestic Karri trees of south-west Western Australia. But now it's a tourist attraction. People come to climb it, or to watch people climb it (as we did). I was happy to go up to about rung four, but that doesn't really count.
Now, there must be some trees in Waikato that could benefit from such an addition. And to do so would require a bit of physics and engineering calculation and implementation. I reckon it would be a fantastic project for a student to tackle – pick the right material (please don't poison the tree or choose anything that won't cope with the weather), work out the loading profile, worst case scenarios (e.g. what happens when two large people cross – one going up and one going down), tackle the safety and ethical issues, and so on. And then, to get a grade A+, the student concerned has to be the first to climb to the top!