The sheer number of hypothetical attacks that are possible under these 'random selection' processes means that the network is likely less secure and predictable.
Since basically all existing cryptocurrencies use mining -- and the few proof-of-stake use another "random selection process" -- I would say that we have plenty of extensive, at-scale, real-world experience about networks that use random selection processes. Random selection has its share of problems -- the Great Bitcoin Fork comes to mind -- but the trustee approach has a lot more unknown unknowns.
All of a sudden people start mining blocks that exclude bids/asks to their benefit or to trigger margin calls.
As I pointed out back when the UNL was proposed, centralization allows for transaction censorship. A trustee may exclude a transaction indefinitely; as long as they're a trustee, there is no way to guarantee they'll be tossed out for excluding any particular transaction. Whereas with random selection, assuming everyone controls less than p percent of the block production capability, the probability that the transaction hasn't been included after n blocks is bounded above by p^-n. Since p < 1/2 (otherwise someone has already owned the network with a 51% attack), this means your transaction will be included within very few blocks with very high probability.
All of the random selection techniques discussed here (and with Nxt) depend upon people putting their private keys at risk.
As I've recommended in at least two other threads, you can allow nodes to delegate mining / minting power. Allowing someone to revocably sign over their block production capacity does not require all block production to be channeled through a single dictator node.
All of the random selection (mining + POS / etc ) techniques have potential for forks (even if just for a few blocks) and this potential is highly problematic.
How exactly does the trustee approach avoid forks? If there's e.g. a network split, won't one side of the split see the trustee's offline and elect a new trustee, and the other side of the split keep going with the old trustee? How is
any decentralized protocol even
able to tell the difference between "a bunch of nodes all decided to quit at once" and "we're on the wrong side of a network split"?
Mining results in a kind of centralization and de-facto trustee that cannot be fired
On the contrary, the "trustee" in mining / minting is fired and replaced after every block. Unless the network's been hit by a successful 51% attack, there's at least a 50% chance the new block producer isn't following the same agenda as the old one. It should be obvious how much this limits the damage a rogue block producer can do.
POS requires peoples keys to be kept on line and ultimately a minority of nodes will participate in block generation
This is simply false. As I discussed above, it's totally possible to allow people to revocably delegate the PoS power of their coins while keeping block production decentralized.