Is this the only reason you are inclined to believe all begin with their names written in the book of life? Don't you find it dangerous to build an entire theological interpretation from simply something Scriptures have been quite conspicuously vague about? Just to get this clear - your primary motivation here is to simply ensure an interpretation that little children don't go to hell and nothing else?You must believe Jesus lied, and little children go to Hell too.....
Revelation 20:15, ". . . whosoever was not found written in the book of life was cast into the lake of fire. . . ."
Again, I too am inclined to believe that little children are always saved though I do not have absolute Scriptural validation for it. And I think that's perfectly fine for God to remain intentionally silent over it - for we are capable of corrupting this to extremes had God made a conclusive revelation. If Hitler's mother had smothered him when he was a child, would he be in paradise? Do babies remain babies in all eternity or will they have grown versions - and if so, will we have the same empathy towards their perceived innocence while they were toddlers even in their grown versions?
And most importantly, if we do conclude that all babies absolutely go to heaven when they die and this is God's absolute truth - what stops an ignorant parent from wanting to avoid risking the baby growing up, being found to be unfaithful and so having their names removed from the book of life? What if this parent reasons it's better for the child to be assured salvation while it has it and determines to kill it? And taken to its extremes, wouldn't it then be logical never to have any children at all - for it is better that that man was never born at all (Matt 26:24)?
No, God forbid. I embrace the ambiguity because now it gives us incentive to raise children in a godly way and pray over their salvation through faith in Christ as the most assured option. Again, the ambiguity gives me enough room to not micro-analyze if dead children are elect or non-elect - instead it allows me to look at it the other way around. I simply assume that God so happens to pick from only the elect when He determines babies to die. This way, I avoid all theological contradictions.