Let me answer your question anecdotally. (A data-driven answer would be better, but I don't want to spend very long trawling AniDB/MAL/etc. If somebody does that, I'll award a bounty.)
From the bottom up:
Third, are there any examples of anime that have asymmetrical seasons like this? Recent and otherwise examples would be nice.
- Shokugeki no Soma (2 cours → 1 cour)
- K-ON! (1 cour → 2 cours)
- Monogatari (15 episodes → 1 cour → 2 cours → 1 cour → 2 cours, not counting the 2-hour-ish specials or the movies or Koyomimonogatari)
- Full Metal Panic! (2 cours → 1 cour → 1 cour)
- Kimi ni Todoke (2 cours → 1 cour)
- Haikyuu!! (2 cours → 2 cours → 1 cour)
- Nisekoi (20 episodes → 1 cour)
- Psycho-Pass (2 cours → 1 cour)
- Yama no Susume (1 cour → 2 cours; this is a short)
- Little Busters! (2 cours → 1 cour)
- Shingeki no Bahamut (1 cour → 2 cours)
- Yowamushi Pedal (3 cours → 2 cours → 2 cours)
(This is mostly recent stuff; I haven't watched enough older stuff to have a good sense for how things worked back in the day.)
Second, how often do second or third seasons break from the cour-count of previous seasons? Does it happen at least once a year, or is it uncommon enough that the last time it happened was ages ago? Does it even happen at all?
The list above is just the ones I remembered offhand as having "asymmetrical" seasons while I was scrolling through the list of anime I've seen. And, alas, I have not yet achieved my lifelong dream of watching literally all the anime, so there are naturally going to be others that I didn't notice.
I'd say this is the kind of thing that happens maybe a few times a year or so - it does seem to be infrequent relative to "symmetrical" seasons, but not so rare as it seems to you. Certainly not something that hasn't happened in ages - Shokugeki no Soma's second season was Fall 2016, and Shingeki no Bahamut's second season is starting soon, in Spring 2017.
First, is there a particular reason for this, or is it "just tradition"?
Here is one clear reason this would happen:
- Long-running cash cows aside, the number of cours in a particular season of a particular anime is a small integer - almost always 1, 2, 3, or 4; and most frequently just 1 or 2. Even if anime season lengths were randomly either 1 or 2 cours, we'd expect to see 50% of two-season anime be "symmetrical". In reality, there is a moderate bias towards 1-cour anime (at least in the present day), so that even absent other factors, we'd expect more than 50% to be "symmetrical".
Additionally, I can offer the following speculative thoughts:
- Some varieties of anime intrinsically lend themselves to particular cour lengths.
- Many sports anime, for example, are structured as a series of tournaments, each of which features a number of competitions, with each competition taking up multiple episodes; this is typically the kind of thing that lends itself to having a tournament per season, with each season consisting of 2 or more cours.
- On the other hand, comedies that aren't Gintama seem to fare best when they don't drag on for too long, biasing them more strongly towards 1-cour seasons.
- If you have an anime that's based on an ongoing manga/novel source, structuring it as a bunch of 1-cour seasons seems to be an effective way to both 1.) avoid running out of source material; and 2.) avoid having long gaps without an anime. Natsume Yuujinchou strikes me as a quintessential example of this.
- If you have an anime adapted from source material that has a regular/predictable narrative structure, and you successfully adapted it into an n-cour anime season, it stands to reason that its next anime season would probably also be well-served by an n-cour run.
I think we see a number of systemic factors that bias multi-season into being "symmetrical" and no systemic factors that bias them into being "asymmetrical".
Of course, on a case-by-case basis, there will often be factors that make it make sense to have "asymmetrical" seasons. For example, with K-ON!, the first season was so enormously successful that the production committee would've been fools not to ride that cash cow into the sunset. And as for Haikyuu!! - while it does follow the "2-cour sports anime" format for its first two seasons, the thing is that its second tournament is long enough that they just split out the most exciting part of it into a separate season, which seems reasonable.