First, to clarify: what I meant by "your" was an entity like a standards community, not an individual, and by "often" I meant within a timeframe that makes bruteforcing parameters infeasible (which itself changes over time wrt the size of the parameters). Key rotation for example is just good practice.

Nothing that I said was wrong - nor does it contradict Colin's advice - and while simple systems are better, that's a tradeoff that should be made if you care about entities with lots of resources like e.g. the NSA. As history shows, bad parameters (or parameters that are feasibly bruteforced over a particular timeframe) are not an 'unlikely' weakness. Besides, being aware of potential vulnerabilities - especially those that you know pose real threats - and not addressing them is simply bad practice.