When the fasten seatbelt signs are off, you are free to roam around the aircraft.. so i see no reason why children cannot sleep on the flood during that time.
Personally, I always take car seats with me aboard aircraft. A pain to lug around airport.. but a blessing once on board!
re; kicking pasenger infront.. hard to avoid.. i try discipling child to best of ability.. not an issue once kid falls asleep..