The key issue here is that there is little to no punishment for actively not trying your best to succeed in the 4 major North American sports; in fact via the draft (and depending on the sport), teams are often rewarded for throwing in the towel completely.
Such an issue does not exist with soccer or rugby, for example. If you tank a season you aren't rewarded the following season with the best college/high school/international player available; you're relegated to a lower division, where prize money is lower, attendances are lower, TV money is lower, the ability to sign high caliber players is lower, and there are no means to qualify for continental competitions (the Champions League in soccer or the Heineken Cup in rugby union, for example) which is where the biiiiiiiiiiiiiig bucks are.
There are numerous examples of teams enduring catastrophic falls from grace as a result of this. A team getting relegated from the Premiership to the Championship in England is estimated to be making something in the region of 25-40 million GBP per season less. Add that to the exodus of players who have contract clauses that grant their release on relegation, and those that simply are too good and are bought up by bigger clubs, and the downfall is not hard to envision from there - the team with no money loses its best players and isn't making enough money to replace them, and you cannot just give up on a season as you will end up falling down yet another division, where again the circumstances become worse still, so you spend what little you have in a desperate attempt to right the ship. Sometimes the ship is indeed righted; sometimes it sinks. Sometimes it sinks spectacularly; Nottingham Forest and Stockport County come to mind.
However, if an NFL team manages to go 1-15 in a season, what happens? They get the first pick in the draft and endure a couple of home games that season where the stadium isn't completely sold out. So? The constant search for parity in American sports, while in many ways is a positive thing, also creates a lot of problems. This would appear to be the largest to me.