Worth worrying about
Latency
Dedicated servers are usually always provided by big game hosting companies, with massive bandwidth DSL connections. They have direct access to the internet backbone providing upload speeds in excess of 100 MBits/s. Now lets scale that back to the average user, lowest tier access to the internet with low priority connection, upload speed generally around 0.5-1.0 MBits/s. I don't know about you but that is not at all good when compared to what game server hosts provide, a 99% reduction in bandwidth. I realise this won't result in a 100 times worse connection, but it will definitly increase ping, if you are in the same state or country you will likely get a ping of 100-250 milliseconds, different state or country? 250-1000 milliseconds seems about right. This would result in awful hit registration and lag. This alone would make competitive play extremely difficult and public play very unpleasant.
Host drop out
The host of the game leaves for whatever reason, and so bang goes the game. I know IW will likely put in some feature that makes another player in the game a host, but this will most likely be not very good and may not work all the time, and in the best scenario would result in a delay in play. This is unacceptable, it disrupts and destroys gameplay and would destroy competitive play. Unless you have a poor server, the game will always be on with no disruptions.
No more big games
You won't be able to have big games without a dedicated server because of the Latency and performance issues mentioned above. The average person's connection just won't be able to handle it, even small games will suffer without the bandwidth of a dedicated server company.
No Mods, maps, hence no modding community
You won't be able to use third party maps or mods as there are no dedicated servers to put them onto. No competitive mods, no competitive gaming. Can't install mods? Then there will be no point in making them anymore so a whole group of people just die out.
Biting the hand that feeds IT
