I don't know if airlines do (or if they care, I suspect that the cost/minute of a 747 twiddling its thumbs is slightly alarming); but I'd be interested in whipping up a little hobby project:
For years (probably decades or centuries if you count more primitive or creative attempts) Delicate and Expensive gear(like, really delicate and expensive, not 'some extra bubble wrap and write 'do not drop' on it delicate and expensive) has been shipped with instrumentation. Fairly basic versions are mechanical, with a chamber that contains sand or beads and an adhesive-coated area where the sand will spill if tilted more than a certain amount, and then get stuck in the adhesive. You stick one or more on the package, and away it goes, and (short of falsifying the label, and possibly the ones you also stuck inside the box, uniquely serialized, etc.) the shipper can't worm their way out of any claim that the package was ill handled.
Something like Maxim's (no not that Maxim, but boy did my parents give me a funny look when my first subcription to "MAXIM: IC Design and Evaluation Guide arrived...) 'Thermochron line extends the sensor capabilities to heat and humidity (logged over time, at adjustable intervals, battery backed RTC). The proliferation of cheap accelerometers and mics for cell phones and the like would presumably be amenable as well...
The point that I'm rambling toward is, with today's tech, and modest volume, a little logger box that provides a complete log, at intervals of a minute or less, of temperature, humidity, orientation (light intensity and magnetic fields if you care), and also logs any tilt or shock excursion conditions, with timestamp, every time they occur, should be something you could get knocked together for under $100. Probably under half that.
Obviously, there is only so much one can do against the sheer indifference of a multinational corporation who can make you wade through every form, EULA, call center flunky, customer service flack, and (if you push them) lawyer) before they'll help you; but the quality of baggage handling might well...improve... if it became customary for people to upload (in some reasonably standardized and easily infographicated format) the treatment their baggage had received when they pick it up from the conveyor after a flight(the logger could probably use bluetooth, and do it right from your cellphone if cables are too old school for you...).
The classic sticker-full-of-sand (from a recognized maker of the same) is a good compliance tool for high end shipping; but you'd need something cheaper, more reusable, and more featureful, if you wanted to work on a broader scale.