It's exactly this scenario that annoys me in the situation a pax is late due to traffic/unavoidable delay, the airlines will frequently not care or assist.
Trouble is that it really can't cut both ways can it?
If the crew aren't there, and it is their own fault, whether it be not allowing enough time for the traffic, or simply sleeping in, the repercussions upon them can be rather more than just missing a flight. Demoted, fired, or losing roster priviledges are all possible outcomes. At the very least they are likely to be replaced by a standby (if one is available), and so drop the trip unpaid.
Generally of course, the crew are there, and with quite a bit of time to spare. On the other hand, on most flights, some passengers would be running late, for a variety of reasons. Waiting for them, each time, even for a small number of minutes, could have extreme repercussions. In London, for instance, even a short delay will cost you your slot, and may mean a long wait. Such a delay has even put the crew into excess duty times and the flight has ultimately not departed. Same thing happens westbound out of Asia. That last person hanging around in duty free has cost me my 'bobcat' (Afghanistan) slot more than once.
Domestically, small delays cannot be made up, and will generally compound on a busy day. And again, the spectre of the crew running out of hours can easily become part of the equation. And even if they don't, it just gets way too messy.