Congratulations!
It wasn't so long ago when I was a newly minted dad. Now my daughter's turning 11. I must agree, in my experience, I was using shorter focal lengths when she was still a baby, when all she did was smile, laugh, try to crawl, and burp. You'll need to be up close, and you really won't need faster glasses. So, a 20-40 will be great for that stage.
The moment she started running, I knew I needed faster, longer lengths, or I needed to learn how to use flash. She would be up close, and at the very next second, a few hundred feet away. A 70 or 77 would be great at this stage.
By the time she started schooling, and stage practices and plays were the order of the day, the need for faster and longer lengths became more pronounced.
And as she enters pre-puberty, things begin to slow down now, and my FA20/FA43 and FA77 are probably all I need now.
So, I guess, you'll need different glasses at different stages. I guess, that's what justifies LBA