Correct - I'm not disagreeing with your assessment of what happens when a firefighter is missing, lost or requires extrication. However a firefighter down doesn't mean the firefighter is always missing, lost, or requiring extrication - it includes being injured on calls.
For example, say two firefighters suffer chemical burns at a warehouse fire but everything else is going according to the IC's plan- an additional alarm would not be called for (you'd definitely get a safety officer if they weren't already present, medics, a replacement company and possibly a few more support companies).
My original point was you would need two call levels, one for an injured firefighter and another for one with floor/roof collapse,
Ok, I didn't mention an injured or burned firefighter, while those could also be missions, I mentioned a DOWNED firefighter. Meaning a situation that a MAYDAY would be declared and the downed firefighter would require some form of extrication by other firefighters.