LEM and others...
It is simply GOOD AIRMANSHIP to put your hands on the thrust levers after TO and this until 10.000' or autopilot engage, whichever is later. Anyone NOT doing this will get a remark in my book. Why on earth would you have any problem with this?! As you fly the B737, you must know that you can not by any means trust the autothrottle 100%. At Sabena, we called this GOP. Good Operators Practice.
Are you talking about guarding the throttles or holding on to them? If you are so concerned about the autotrottles, why don't you keep your hands on them all the time? Which book are you putting your remarks in? Is this SOP in your new airline?
Also regarding the FD... It is a GUIDANCE tool and NOT an ORDER bar.
This simply means that you should never BLINDLY follow the FD. Boeing says that on the B737, any pitch of 22.5 degrees or higher is exessive, yet the FD often asks you for a higher one. It merely wants you to keep speed. NEVER EVER (exept if ground contact is imminent or severe windshear) go beyond 20 degrees pitch on the B737. So what if speed goes up a little bit. Better this than the opposite.
On a normal derated take off I've never seen a FD command 20 degrees+. On the other hand, I have never seen a 20 ANU limitation anywhere either.