On the TSA website, their "tips for packing your checked baggage" twice emphasizes that you shouldn't over-pack your bags:
Avoid over packing your bag so that the screener will be able to easily reseal your bag if it is opened for inspection. If possible, spread your contents over several bags. Check with your airline or travel agent for maximum weight limitations.
Avoid over packing so that your articles don't spill out if your bag is opened for inspection.
How common is it for baggage inspectors in the US to open bags and rummage around deep inside? What happens if you have a bag packed to bursting and they're not able to easily close it after inspection?