Was European colonization of the New World beneficial?
The answer to this question revolves around another question; "beneficial to who?"
If we are talking about the Native Americans, the European colonization of the New World was in no way beneficial. The colonization killed off a huge percentage of the natives who were living at the time of European contact. It took away the natives' land and made them, at best, second class citizens of the new countries that were created.
For the Europeans, and indeed for us today, the colonization was beneficial. They benefitted (and we benefit today) from the riches of the New World. In the United States, we are able to live in freedom because the colonization of the New World helped to lead to the rise of democracy in what is now the United States.
So, the legacy of European colonization is very different depending on the point of view from which we look at it.