There's simply too many players for them to use dedicated servers. Just on XBL alone, the past three or four CoD games are in the top 10 most played/active list with millions of users. Factor in all platforms and it's absolutely not cost effective from a business standpoint.
Additionally, dedicated servers will NOT stop lag or the infamous lag compensation problems that are the most outspoken problem in the CoD series. It's a software issue that the developers need to address, but it's unlikely it will ever happen since the game sells so well even with these problems.
Check out
http://m.youtube.com/#/watch?v=ZoFnIckyoxg&desktop_uri=/watch?v=ZoFnIckyoxg
One thing I will say is IW has at least always acknowledged the issue and tries to adjust it in every patch. Treyarch on the other hand has NEVER acknowledged it as a problem and instead pinned the blame on the consumer and their ISP - that's on top of their smug, disgusting attitude about the issue. I learned my lesson with BO2 - no more Treyarch games ever again.