Why limit the bank angle to 10° when passing through FL300 on a B737-800?
One reason that comes to mind is as you get closer to the coffin corner, the extra G force due to maneuvering could cause a stall.  Quoting from "Stall the Pig",


  In the thin air at altitude, jets operate within a very narrow
  airspeed band between MMO (redline) and the low-speed limit, typically
  a yellow arc that provides a warning zone prior to a stall, indicated
  by a lower red line. At high altitudes and high weights, this
  band—known as “coffin corner”—can be quite narrow, leaving you a mere
  10 knots of usable airspeed range, for example. Load up the wing in a
  turn and that lower redline will quickly move upward toward your
  airspeed.


By limiting the bank angle, you also limit the G forces, and stay farther away from an accelerated stall.