I think I can totally answer your concern. I go with my daughter (4.5 yrs but always take bb car in Japan) In HK, she doesn't need BB car for 1 yr.
in 新宿, Most exit has NO lift and escalator. But I ask Japanese man to bring the car because most of time my daughter was sleeping. Remind : Only 新宿 is like that. Other stations has lift because I always 轉車. Although 新宿 mostly exit No lift, 1-2 exit has -- My city & 小田急. But you are sure you are familiar the 新宿 station, you can find where is My city & 小田急. I find that in my 3rd day. ha.... !!
Bring BB car is necessary (MUST) and have high priority to go first -- 登機, 日本check in, any where. In disnery BB car, it can't adjust the level. My daughter all the time to lay down on bb car during taking JR. Even going to toilet, I put BB car outside, no one get my car. Because their bb are almost 90% are COMBI / Aprica ($3000) expensive than me.
Sure ! Don't bring heavy BB car. Don't buy BB car in Japan as it is more expensive than in HK as I check the price from Toy'R.