It is almost logically impossible to prove the destruction of the secret seed. And if it is destroyed, then it is infeasible to verify its entropy. It's a magic number, and as such can be chosen to create vulnerability.
The way they propose to do it, I fully agree with you. However, I think the issue is not entirely hopeless. There are a few conditions, and I don't know if they can be satisfied, but if:
1) the pool of key generators should be large - say at least a 1000 members, in such a way *that everybody who wants, can participate*.
2) the entropy of the total key will be at least the entropy of each individual contributing key
3) each participant can see many other participants (maybe not all, but many of them), and each participant can check that his contribution is part of the final result
then I think the trusted setup can work.
For instance, suppose that one uses a known communication channel - say bitcointalk.org - where people can sign up and POST their contribution (the public key contribution, not their to be destroyed private key of course). YOU CAN TOO.
When, after sufficient time, the number of needed participants is reached (can this be variable or is this fixed from the start ?), the final keys are publicly calculated from the posted ones. You can do that too, including your own key of course. We should all agree upon the resulting keys, and we can all verify that all key shards have been included, including our own.
Now in as much as we know of ourselves that we destroyed (or at least kept secret :-) ) our secret key, we know that nobody has the golden key. And in as much as we DO collude with all the others to make a golden key, then we also know that at least a thousand people, including ourselves, are aware of this and we can make this public at any moment (and prove it: by publishing the golden key, we definitely kill the trusted setup ; we would be crazy not to obtain the golden key in return for our own shard of secret key).
It will be difficult to keep such a secret with 1000 people, and at least EACH of these 1000 people know, and know that the 999 others know.
The point is: *if* anybody has the OPPORTUNITY to be part of the trusted setup, and if the number of people involved is huge, then I think one can trust the trusted setup. But 18 "celebrities", no thank you.
