My understanding of the shakedown is that you want to see if you mounted everything right, are all the electronics wired correctly and so forth. I doubt anyone really identifies a massive mechanical issue that needs a week to fix.
Why do teams do the shakedown earlier nowadays. I would wager that they are doing it because the cars are reliable so no real risk of reduced running on first proper day of testing. Other reason is to get early and quick correlation data - Mercedes was running aero sensors and they are feeding back that data a week or so earlier than McLaren will.