What effect might Titania's sleeping presence have on other actions in A Midsummer Night's Dream?
Titania remains on stage asleep from the time the fairies sing the lullaby until Bottom wakes her up. This means she has to be in a place where she can be seen without her presence being disruptive. Off to one side of the stage is best. There is supposed to be an “invisible” area of the stage where Puck and Oberon can go to be invisible.
There is a practical reason for Titania to be on the stage—other characters do interact with her. Oberon anoints her, for example.
[Exeunt Fairies, Titania] Sleeps
Enter Oberon [and squeezes the flower on Titania's eyelids] (Act 2, Scene 2)
Another reason for her presence is that is serves as a reminder that all of the action taking place in this part of the play is influenced by magic. This is fairy time, and the fairy wood. The humans are just encroaching on fairy territory.