yes you are wrong. Walima is a sunnah and there were a number of different ways in which the Prophet (pbuh) conducted Walima with his marriages, not necessarily after consummation.
the way in which people do nikkah now on a ‘barat’ day with lots of guests, walima as a seperate event is almost redundant islamically. nikkah is done and if the groom pays for the food for the guests he has fulfilled the sunnah of walima. in fact a lot of scholars recommend this, in this day and age.