I don't think they do.

I know around here it seems like everyone and their dog is at least gold or equivalent and we keep ourselves out of the know by hiding in lounges where one wouldn't often find non-elites with the exception of the occasional splurger.

But really most leisure travellers have no status at all, and aren't even a member of an ffp at all. Depending on the season, this is easily many an airline's largest customer base. Around here we know them as kettles, and there are lots of them.

These are the people these charges were designed for: they want lower prices, or they just won't fly (they'll go somewhere closer instead). Of course they then didn't figure out that that money had to come from somewhere.

Indeed, the actual frequent flyers still get that free bag as part of their elite benefits. But that isn't most people on the plane. Most people on the plane have to pay the charge. And don't want to. So they cram it all in their carry-on to avoid it. And everyone else suffers for it.

I won't say the problem will go away completely just with a 'free' first bag (paid for in the ticket, of course). You're right: reclaiming baggage needs to be sped up for that, too. The process needs to be as effortless for the pax as possible. But I truly believe that a 'free' first bag will relieve a large part of the strain on many flights.