They're powerful because they can "load the dice" and so make the distributed system more intuitive for humans to reason about, more resilient to real world faults, and do all this with more performance.
For example, Barbara Liskov and James Cowling's deterministic view change from VSR [1][2], which isn't plagued by the latency issues of RAFT's randomized dueling leader problem. VSR's deterministic view change can react to a failed primary much quicker than RAFT since heartbeat timeouts don't require the randomized "padding" that they do in RAFT, commence the leader election, and also ensure that the leader election succeeds without a split vote.
Determinism makes all this possible.
Deterministic testing [3][4] is also your best friend when it comes to testing distributed systems.
[1] An introductory talk on VSR and it's deterministic view change — https://www.youtube.com/watch?v=Wii1LX_ltIs
[2] James Cowling on determinism, working with Barbara Liskov — https://www.youtube.com/watch?v=ps106zjmjhw
[3] FoundationDB are pioneers of deterministic testing — https://www.youtube.com/watch?v=OJb8A6h9jQQ
[4] TigerBeetle's deterministic simulation tests — https://github.com/coilhq/tigerbeetle#simulation-tests
Huh? How could a nondeterministic algorithm be predictable? Do you mean algorithms with a nondeterministic but overall irrelevant component ("pick a random element from this set")?
Example: size of a set = 1 + (remove an element from the set and then compute size of reduced set, or 0 if set is empty)