In my opinion, the way anime is meant to be watched, is one episode every week. Anime is something niche, and word of mouth can spread only if it runs for a significant period of time, in this case, 13 weeks.
Seasonal anime have become popular because fo the rise of internet, reddit and forums. Since no one has seen the up-coming episode(like duh!), it provokes discussions and fan-theories, that leads to the anime becoming popular. That's how Attack on Titan became popular. Yes, the source material was already popular, but the anime took it to new heights. I think that 2006, 2007 brought a radical change to this sort of thing. You can look up the anime that aired during those two years(Death Note, Code Geass, Guren Lagann, Haruhi, etc.,).
An anime usually runs for one cour(12-13 weeks) or two cours(24-26 weeks). You are confusing seasonal anime with second season or third season of an anime. Seasonal anime run for 12-13 weeks, from January to March(Winter), April to June(Spring), July to September(Summer) and October to December(Fall).
As I already mentioned, they may last one season(13 weeks) or two seasons (26 weeks).
To give you an example, Code Geass season 1 began in Fall 2006, and ended in Winter 2007. Code Geass Season 2 began in Spring 2008 and ended in Summer 2008. So, the second season doesn't air in the exam same season(i.e., Summer, Spring, Fall, Winter). They release it when it's ready, and also it includes a slew of marketing stuff.