What do you mean by "failed task executions"? Do you mean jobs?
Currently, the last exception message and stacktrace is stored in the ACT_RU_JOB table, until the moment the job is executed again. When successful the second time, job disappears, if not, new exception is stored. We currently don't have plans to add this in the history. Currently, the history contains process-stuff that happened in the past. Failed jobs didn't actually "happen" when you look at it from a process-perspective, since process-state is unaltered and transaction is rolled back on failure.
You can always build a custom solution, by wrapping the existing JobHandlers and logging any exceptions occurred in your own solution.