Or, y'know, you could just let the 162-game season speak for itself and not fuck around with wild cards and expanded playoffs. But that's heresy.
Most soccer countries run two (or more) concurrent tournaments. England, for example, has the league championship which is a 92-team stack divided into 4 divisions - the top division being the Premiership - with promotions and demotions between the divisions at season's end. Winning the "league" is the most prestigious trophy, because it is the hardest to attain.
Alongside that, and intermingled among the league fixtures over the season, are knockout competitions. The FA Cup, for example, starts at the beginning of the season and involves any team with a suitable venue who plays in an FA-sanctioned league. There are 14 rounds of single-elimination games - home team decided by whose name comes out of the hat first. There are no seedings, except that the teams from the lower 2 of the top divisions come in at the 7th round and the top 2 divisions are fed into the competition at the 9th round. Blind draws for each round mean that a "non-league" team can get a trip to Old Trafford just as easily as Spurs can draw Arsenal in their first match.
There is a third domestic competition, another knockout tournament, involving only teams from the top 4 divisions, being the League or "Carling" Cup. It runs parallel to the others and on the same format as the FA Cup. All three competitions can secure a place in the following season's European tournaments, being the increasingly mis-titled Champions League, and the second tier Europa Cup, both of which are hybrid league and knockout tournaments.
The upshot of all this is that, regardless of how shitty your team's season is, there is a very good chance that you have a very important match coming up at regular intervals. Bad teams are battling against relegation, while trying to bolster their mood (and coffers) with "a run" in "the cup", be it domestic or European. Good teams stay alive in all competitions, and then have to deal with a pile up of fixtures. Even the best teams struggle to win two or more trophies in one season due to the fatigue and stress of all the "big" matches they play.
I have always found it odd that US sports make teams slog it out for a whole season (16 or 162 games or whatever the NBA/NHL do), and then reset everyone to zero for another tournament to decide the best. Didn't the league play already decide that?