I just don't see why you guys find it distracting. It is literally an integral part of the theatre experience.
Many entrances are designed specifically FOR entrance applause - Elphaba in Wicked is a GLARING example, as when she runs downstage out of nowhere, staring dreamily into the balcony, she seems to quite literally embrace her own entrance applause. The music and moment before her entrance are also synced dramatically to stir audience applause, as Glinda introduces her ("...in school!") and the music crescendoes blissfully.
The fact is, an entrance is WORTHY of applause. It is an entrance, and entrances are dramatic. You will find that even in movies, when a celebrity or star is first displayed, a good director will have designed a dramatic way of framing him or her for the first time - perhaps he or she turns to face the camera, or his or her hands are viewed first, or feet walking on the street. A kind of suspense builds up as an audience prepares for a star's first appearance.
If a director wants to avoid entrance applause altogether, so as to maintain the flow of a scene, he or she will find some way to avert it. But you'll notice that when it occurs, it occurs because a place has been deliberately created for it in the staging of the production.
"I am the sound of distant thunder, the color of flame."
CARRIE the Musical