Thanks for the rundown, Cnut, I definitely get that seeding matters in a way, but I know in football most teams don't really care since the performance of all teams tends to mean that supposed giants end up in a lower seed, and every season, unexpected underdogs who won recently end up in the highest seed pots.
True, but you don't want the big players to end up playing each other in the first round, you want to save it for the later stages of the tournament (especially if you're running the tournament). I'd also argue that tennis seedings are generally more accurate than football seedings, because their performances can more easily be compared, e.g. Djokovic and Nadal are playing the same set of opponents and same level of tournaments each year, in a way that say Poland and Colombia in football are not. Another point is that tennis matches come quickly after each other. Going back a few years, if you had Djokovic, Nadal, Federer and Murray all in the same half of the draw, then whoever got to the final would be exhausted and quite possibly lose to a lesser player who's had a much easier run-in.
One last question, seems it doesn't seem easily Google-able: if rankings are only from how far you get in a tourney, you don't get extra points for playing/winning more games to get to the same stage as a seeded opponent who doesn't need to play earlier stages?
ATP and WTA differ a bit, but ATP rankings are as below (from the Wikipedia page, easier to post as an image than text!). Getting through the qualification tournament will get you more points (e.g. 25 points for getting through the qualification tournament for a slam), but otherwise no, you don't get extra points. So for example a seeded player who loses in the first round of all four slams gets (4x10=) 40 points. If you're a lower ranked player, you'd have to get to R16 in two ATP250 tournaments to get the same points haul. But I don't think this is unfair at all... the reason being that for top players, 10 or even 100 points here or there is largely irrelevant to their ranking, whereas if you're outside the top 100, even 10 points can be a big deal (e.g. compare Berrettini ranked 10 on 3,805 points, with Thiago Montiero ranked 100 on 651 points).
https://en.wikipedia.org/wiki/ATP_rankings#Ranking_method