Why do so many sports leagues use play-offs?
Because a play-off manufactures a decisive, high-stakes single event at the end of the season — which is commercially valuable and dramatically satisfying, even though it is a worse method of identifying the best team.
The tension, stated plainly. A league table over a long season is a far better measure of quality: many matches, home and away, everyone plays everyone, and luck largely averages out. A play-off is a small number of matches in which the better team frequently loses.
So the two formats optimise for different things — accuracy versus drama — and leagues choose accordingly.
Why play-offs are used anyway:
They create a final. A single occasion with a definite winner, in front of the largest audience of the season, which is worth a great deal in broadcast and sponsorship terms. A league won with three games to spare produces no such moment.
They keep more teams interested for longer. In a pure league, mid-table teams have nothing to play for by spring. A play-off place extends meaningful competition down the table and sustains attendance and viewing.
They accommodate large, geographically divided leagues. North American leagues with conferences cannot have everyone play everyone equally, so a play-off reconciles unbalanced schedules.
They suit sports with short seasons, where the regular season sample is too small to be authoritative anyway.
Why European football largely resisted them for the championship: the league title is treated as the authoritative measure, and promotion and relegation already supply jeopardy at both ends of the table. Play-offs are used for promotion places specifically, which is where the drama is wanted.
The hybrid approaches: seeding play-offs by regular-season finish, so the league still matters; giving the top team a bye; home advantage through the play-offs for higher seeds; and best-of-seven series rather than single games, which substantially increases the chance the better team advances.
The honest summary: a longer series is more accurate, a single game is more dramatic, and every format is a negotiation between those two.