I mean.... there is a reason why riot releases new champions at 7800 IP for the first week, to decrease the competition of those who want to play the champion. After a week they are reduced to 6300. The three week wait after champ release before being put on rotation is to further respect those that bought the champions.
Within 4-5 months every champion will be cycled even if it just once, however riot has to pander to the newer players as well as pay attention to the popularity of certain champs over others. League has approximately 140 champions, and each rotation is approximately 10 champions (sometimes more [e.g. when they tried to increase support popularity] but usually 10) therefore thats approximately 14 weeks, which is approximately 3 months, if you cycle each champion without repitition. Therefore if you account popularity, ease of play and new players then yh, it's understandable that it can be 5 months.
As for why it's not a "pick a champion out of 136" but rather "pick a champion out of 10" because psychology has proven that humans find it difficult to make decisions when a multitude of options are given, free rotation gives a safe zone for new players to experiment.......and sure u may counter with "then give some suggestions instead" but remember, riot is also a business, they know if you really want to try a champion then u'll do it with IP or RP, instead of waiting.
And Riot did explain why free week rotation was structured that way in several different posts and even a Dev/r. If you google it u should come across some (or just look through the history of dev/r or the boards. Here is one: http://forums.na.leagueoflegends.com/board/showthread.php?t=46045