Why no pesukim before havdoloh (and kiddush) in Shul?

Why do we start with Hinei Keil Y'shuasi at home but not in shul?

MPerlman

Those pesukim are not part of the essence of havdoloh. They are just pesukim that were added later on by some.

Similarly, on Friday night when kiddush is made in Shul, the pesukim at the beginning, before borei peri hagefen, are omitted as well.

I think they are left out in Shul since they are not part of the essence of havdoloh or kiddush, and because tircha detzibura is involved in adding recitations. At home, people have more freedom to add on.

Litvak

Vaychuylu is not said during kiddush in shul because it is said immediately after the tefillas sheva of Maariv. Chazal instituted it at home before kiddush to be motzi those at home who didn't say vaychulu. I believe that there's a story brought in the Maharil that he forgot to say vaychulu before kiddush, and upon remembering in the middle of the meal, poured a new cup of wine and recited vaychulu upon it.

Melech