For the past two years, I have given my son and his family a yearly zoo membership and am planning to continue this year. I also give them each a couple of surprises to unwrap. We do our best to focus on "experiences", not "stuff".
My DDIL is the youngest of 4 sisters and there are 22 people in their giving group. There are 2 drawings for names - one for the adults and one for the children. This system has worked well for them for years.
My holiday traditions have gradually changed and simplified over the years. Thank goodness!!! Younger generations want to create their own traditions. Both of your daughters "want to draw names this year in an effort to simplify things." I think the core of the previous sentence is - "Both daughters want to simplify." Perhaps the best Christmas present you could give them this year is to go along with their request.