It's just an example, trying to understand how a random function would work.
Simple.
The entropy for the seed would come from the proof-of-work hash that wins the block. All other validators would respect this entropy.
Let's say randomizing numbers is out of the question.
It is not out-of-the question. The randomness of a number is determined by the source of the entropy. Proof-of-work has a high entropy.
No, because you can't check time either, so you can't write that program!
Hmmm...
a) That sounds extremely crippled
b) That sounds extremely broken if the result is ...forking (I'm not sure that it can keep things deterministic when there are tens if not hundreds of possible triggers for indirectly randomizing things).
The primary reason that smart contracts are basically useless, is because a block chain can't form a consensus about anything external, except for signatures transactions that are authorized by public key cryptography to modify block chain state. Block chains can only form a consensus about block chain state transformations with the clock period being blocks and the longest chain rule.
If it were possible to introduce state into the block chain that could not be objectively verified by all validators, then the Nash equilibrium is lost, a Prisoner's Dilemma is created, and consensus is no longer convergent.
Augur is an example of attempting to form consensus about external state (the outcomes of prediction markets) by employing reputation of participants. Essentially they attempt to build a new consensus system on top of Ethereum's block chain consensus. But the problem is those two consensus systems can not be orthogonal, because validators of Ethereum have to be able to agree on the objective state on the block chain of Augur data. Notwithstanding that the Byzantine Generals Problem can't be solved with reputation and propagation, due to Sybil attacks.
Everything Ethereum is a delirium. Delusional just like Vitalik staring off into blank space when he speaks.