The randomness will be used to defend against knowing in advance what nodes are responsible for the HSDir entries in the hashring (allowing DoS and statistics gathering). If an attacker knew the next numbers, then this protection would be broken (but none of the other important protections would be broken).
Right, and this answers the parent's question. Currently, the layout of the HSDir is deterministic and therefore predictable by anyone, which allows for a number of potential attacks. See "Non-Hidden Hidden Services Considered Harmful" for context [0].
In the context of using the distributed randomness protocol to randomize the DHT layout, if the protocol were somehow broken then the worst case outcome would be that the DHT layout would again be predictable, which is no worse than the status quo today.
Disclaimer: IIRC there are some proposals to use the distributed randomness protocol for other things besides randomizing the DHT; I cannot speak to how those proposals might be affected if the distributed randomness protocol is flawed.
