This is an interesting question.
Without vayechulu, the brachah on the wine is unattached to any context. Vayechulu gives the brachah that context and perspective. On Shabbat morning there is no set introduction and so many minhagim have developed to put the brachah in a framework. There are those who only say the brachah without the introduction, perhaps because by then, an introduction to shabbat is superfluous.
However, on yom tov we do not have an introduction for context for kiddush at night (and some skip one in the morning)and suffice with starting with the brachah. Why the difference? I don’t know, but I will check it out bli neder.
Bottom line, is it halachically required? No. But I have never been to a formal wedding where the chatan didn’t say “harei at mekudeshet”, even though the context obviously announces the purpose of the ring giving, and if the chatan doesn’t say it, they are still married. It’s part of the package, and it’s traditional and beautiful. So too with Vayechulu.