I'll take you up on two issues here.
First, Arsenal are not "rich". My club is run as a sensible business. Despite some of our shares being owned by billionaires, we do not get one penny from our owners either. We are routinely outspent by other clubs outside of the top four. We survive by bringing in the best young players we can find and turning them in to world class players. Arsenal built a new stadium to support this, at the club's own expense.
Second, the reason we have so many fans is because the club markets itself well and we play entertaining football that people want to pay to see. This is why our stadium sells out every week. We often even fill our stadium for Carling Cup games where the fans know they won't be seeing our strongest line-up.
Football exists for the purposes of entertainment. If you do not entertain the fans then you are ripping them off. Defensive football is one thing, outright dirty football is another, you are not just ripping your own fans off but you are ripping off the entire Premier League when top players are unable to play because they're injured.