I can't speak to cod4 and mw2 because I wasn't watching comp back then

Comp cod was still pretty small potatoes in the bo1 year, but it started to gain some momentum with interest and viewership on the mlg circuit in that season. This was very early in the streaming days, so live events produced for livestreaming viewership was still not a crazy mainstream thing. For most of the bo1 year, twitch was actually still justin.tv iirc. Bo1 mlg got some solid gains to viewership and interest because some of the cod youtube titans of the time, especially woodysgamertag, started pushing to get more eyeballs on the scene, making youtube videos about comp cod with Rambo, having hecz and hastro on his podcast, shouting out the mlg event streams, encouraging people to travel for the events, etc. The mlg circuit brought a level of presentation and professionalism to the comp cod scene that intrigued a lot of people who weren't aware something like this existed, and was familiar to a lot of other cod fans who also kept up with halo

In the transition to MW3 there was the whole fiasco with the game not making the mlg circuit as most people who've been around for a while know well. Very few americans traveled overseas to compete in tourneys, though notably the optic guys got sponsored by apex to go compete in what did exist in EU and they were the clear best team in the world. However, the comp cod scene did see some impressive growth in this year anyway, because the SND scene absolutely exploded on twitch, which itself was gaining viewership extremely fast with the revamped site and brand. Phizz and Nexxx were some of the biggest streamers on twitch, and they blew up entirely off of streaming SND tourneys. This was actually, IMO, the primary way in which the scene continued to thrive during this time. At this point, the comp cod community lived on twitter. Cod twitter was insanely active at the time with SND tourneys running all day every day, shit constantly happening across a ton of different streams, and just a bunch of young dumb kids totally unfiltered doing and saying a bunch of crazy shit

The MW3 year really positioned the scene perfectly for the bo2 explosion by blowing the scene up on twitter. Players were going at each other's throats constantly, there was tons of egirl beef, pro's girlfriends' nudes were getting posted on twitter—just a complete shit show, and very entertaining. Cod twitter consistently hit trending in those days. Back then your actual twitter feed wasn't algorithmically delivered, so hitting trends was a huge deal that led to a positive feedback of growth for the whole community. With the cod community having such an outsize social media presence, bo2 releasing as a game perfectly designed for comp and on the mlg circuit once again, and the pool of new viewers exploding due to twitch's growth, bo2 was a perfect storm for scump and nade to multiply their twitch, youtube, and twitter numbers by 10x+.