Unless you're talking about some
extremely niche tournament, that's not how it works at all, in football at least. In the majority of league systems you get 3 points for a win, 1 point for a draw and
that's it. If you are level on points with another team in your group after all games are played then there will be strictly defined rules for that tournament to separate the teams, often a combination of the following in some order of precedence:
- head-to-head results between tied teams
- total goal difference, i.e. sum(goals_scored) - sum(goals_conceded) across all games
- total goals scored across all games
- disciplinary record (number of yellow/red cards awarded against players)
If teams still cannot be separated, it'll fall back on something as simple and cruel as a coin-toss - though maybe they could go to extra time and penalties if the tied teams are playing each other in the last game. Maybe you're thinking of situations like rugby where you can get a "bonus point" games in group stages by scoring 4 tries or keeping the losing margin down to a handful of points.
In any case, I can't give a good reason as to why 3-0 is usually the score given for a walkover - I think it's just generally considered to be a convincing win that isn't too over-the-top.