I'd like to answer by offering a counter-question for you.
I think we can agree that the seconds surrounding the engine start is one of the few really critical moments in getting an airplane off the ground. Sure, the rest is important as well, but you can usually afford to lose a few seconds during, say, the magneto check, or while lining up on the runway for departure.
If we can agree on that, then the question for you becomes: does holding the checklist in your hand during engine start somehow help you start the engine in a safer manner?
Maybe, in some roundabout way, it can be argued that it does. But in this specific case, there seems to be a much more direct argument that can be made that holding the throttle will help you react much more quickly in case, say, it's mis-set and the plane lurches forward when the engine takes.
(You probably should verify that the throttle is set to idle, or very close to idle, before you begin starting the engine, but this is part of the belt-and-suspenders attitude you'll see a lot in aviation.)
When in doubt, always refer to an approved checklist. If the checklist doesn't say, then make a judgement call on what's more likely to make an emergent situation easier to handle, or what is more likely to improve aviation safety, and go with that. If you're having trouble working that out, talk to your instructor. I really recommend getting into the habit of not asking just what to do; rather, ask why to do it in some particular way. You're paying for your instructor's time, and their experience in these matters; as long as you're learning, they can handle the occasional "dumb" question.
Also, the checklist probably calls for you to somehow verify that the engine is healthy immediately after starting it. In the airplane I fly, the immediate check is for the oil pressure to be within limits. It pays to read ahead a little before starting the engine, so that you can proceed immediately with those immediately-after-start checklist items. The checklist is a tool to help you remember each and every step, but you are allowed to read ahead when doing so is beneficial. Just don't forget any of the steps.