There was also the allure of our beautiful national parks to deal with!
Halo 3 was overall incredible in terms of ranking system, general updates, DLC, maps, community gametypes, and just overall matchmaking experience. Pretty much everything
but the basic feel of running around shooting people was great compared to subsequent Halo games. However, you can't ignore that part of its relative success is borne out of the context in which it was released. Similarly, I'm not saying Halo 5 is the bestest-best game ever, but there are a lot of reasons why it didn't take over Xbox Live that have nothing to do with the gameplay.
There are huge differences in the market segment Halo occupies between when Halo 3 came out and when 5 came out. Most Xbox players play shooters more often than other games, which has been the case basically from the beginning. Other genres just aren't that important of a factor. For example, only 3/20 of the top-five games on Live between 2007-2010 are non-shooters by my count (see below).
So, back in the day, the choice for Xbox players was Halo 3, COD (4 specifically), Gears, or some non-shooter. Halo 3 was obviously a superior choice for most people.
That's way different compared to the competition we see today. Some franchises didn't exist yet, like Titanfall or Destiny, or hadn't made a dent yet on consoles like Battlefield. There were no free to play shooters of note and Battle Royale was a manga. COD was only just starting to develop the relentless release schedule we see today (also, see below). How many COD games have been released since Halo 5 came out? You can't ignore the shear marketing power of having a franchise headlining every few months. In sum, Halo's relative niche is much, much more competitive than it used to be.
We're also at the moment coming at this at a unique gap in Halo history. If we transformed Halo 5's post-release timeline into Halo 3's, we would be playing Reach right now. ODST would have been in 2017.
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Most played Live games 2007-2010
2007 (
https://majornelson.com/2008/01/04/top-xbox-live-games-of-2007/ )
1. Halo 3
2. Gears of War
3. Call of Duty 4
4. Tom Clancy's Rainbow Six Vegas
5. Call Of Duty 3
2008 (
https://majornelson.com/2009/01/04/the-top-20-live-games-of-2008/ )
1. Halo 3
2. Call of Duty 4
3. GTA IV
4. Gears of War 2
5. Gears of War
2009 (
https://majornelson.com/2010/01/11/the-top-20-live-games-of-2009/ )
1. Halo 3
2. Call of Duty 4
3. Modern Warfare 2
4. Call of Duty: WaW
5. Gears of War 2
2010 (
https://majornelson.com/2011/02/03/top-xbox-live-games-of-2010/ )
1. Call of Duty: Black Ops
2. Halo: Reach
3. Red Dead Redemption
4. Fable III
5. Battlefield: Bad Co. 2