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David's description applies to shipping companies that do all their own air transport themselves.
The alternative method for mail and small items is for the shipping company to pay a budget airline to carry crates of mail, and at the destination airport a shipping company employee receives the crates airside. This is why hold luggage costs so much on budget airlines: less luggage, more money from carrying mail.
Airlines are still flying empty planes to ensure they don't lose their takeoff and landing slots and to keep pilot hours up.
Must be heavily affected by covid though, German parcels to me have for years been very quick. Anyway I’ll shut up now.