Your anecdotal scenarios included precisely zero examples meeting that situation. The reality is, without pre-planning, dealing with either country's entry requirements can be an exercise in frustration unless you prepare. The prevalence of real-time entry eligibility checking at the gate-bridge has moved the importance of understanding what you need to do.

If you're traveling to Australia for example, your eligibility is determined when your passport is scanned at boarding. You scan a US passport on departure from SFO for example when you have AU citizenship, it will flag "DO NOT BOARD" because the Department of Home Affairs systems will say that individual has no ETA, and if that individual tried to apply for one, it would be refused (due to being ineligible as a citizen) while if you scanned another passport, the I-94 records will be way out of whack and cause issues for re-entry, since the US uses APIS as a primary source of exit data.

Some countries (cough, the US) use check-in/APIS data in lieu of exit immigration. Your departure is as important as your arrival. There's a reason that ICAO has a working group sorting this. Because right now it's a mess that unfairly stings travellers. Especially dual-citizen ones.