A national symbol is something that people can rally around. It catches attention and spurs emotion. Our symbols are part of how we communicate who we are as a people. While they may seem to have no practical use, they are valuable in the sense of community they help people have.
Yes, nation symbols matter. They help create a cultural icon for the country that people in other countries can think of when they think of those countries. National symbols are something that members of a country can take pride in. They make countries as a whole seem more friendly to others.
I believe that national symbols are critical because they unite citizens around a common image and therefore a common identity. This makes communities stronger because everyone identifies with the same imagery and what that imagery represents for them as a nation. So yes, I do think that national symbols matter.
The unicorn being Scotland's national animal is hilarious. How many people in the world even know their's or countries' national symbols? They are of no importance, except perhaps for ultra patriots who want a terrible tattoo? They are generally outdated symbols that once had meaning but are probably just used as stereotypical images now.