Do most amateur players play aggressively?
That's a very broad and sweeping generalization because, for a start, the vast majority of chess players are amateurs. Very, very few are professionals. Very, very few can actually make a living from chess by playing, coaching or teaching. Not even all grandmasters can make a living from chess.
Then there is the biblical saying (from Ecclesiastes / Kohelet): "There is a time and place for everything under heaven." as immortalized by Mary Hopkins. On the chessboard too there is a time for aggression, a time for quiet development, a time for prophylaxis, etc., and a good player will be aggressive when the position calls for it.
So, I suspect the answer is "No", although it is probably true that most very weak players are over-aggressive. To understand why, it's worth looking at the major factors which separate very weak players from strong players:
- Strong players understand one of the core principles of opening development: "First develop your pieces (trying not to move any piece twice until all the pieces have been developed) and only then think about attacking." (Nimzowitsch: "My System")
- Probably the biggest difference between strong and weak players is not calculating ability but the ability to correctly evaluate a position. One of the saddest ways weaker players lose to stronger players is by doing some calculations and evaluating the resulting position as equal while the stronger players evaluate the position as materially equal but positionally crushing. That position is duly reached and the weaker player is crushed without ever knowing why (unless they ask the other player during the postmortem). Hint: when you lose to a stronger player in a serious game always ask for a postmortem if there is time.
- Strong players play prophylactically (again Nimzowitsch: "My System"). Once past their opening knowledge they continually ask after every opposition move "Why was that move played? What are the plans? How can I stop them?". The weak player rarely does this unless the opponent makes a very obvious move threatening a capture or mate.