Agreed, no argument there. But you’ve just described a small mass casualty incident, and I was talking about every day. In my real but admittedly suburban world, when I take an elderly patient to the ER, they go first in line in part because they tend to call with serious conditions and in part just because they are elderly and almost anything could potentially be serious with them.
That, and there are abundant resources to treat everyone who walks, crawls or is wheeled into an ER on any given day.
It's only when resources are scarce (think socialize medicine or a disaster) that real triage (as opposed to scheduling) becomes a necessity.