It makes sense to pick up your bags in WAW, as it's your final destination. You go thru contrôle passeports at your first point of entry into the zone Schengen, which is FRA. Then your flight to WAW will be like a domestic flight, with no further passeport formalities upon arrival there.

What doesn't makes sense is how it works in the US, where you have to pick them up even if it's not your final destination (which could be outside the US).