I agree that the short answer is that it makes more money, but before you go and dismiss it as completely bad for the consumer, I think it warrants a closer and more in-depth look.
First off, I think you can quite readily equate yesterday's "expansions" and today's "DLC." Expansions in the past were new content added onto the old game. As you said in your OP, it was new levels, missions, characters, etc., all bundled into an expansion. Today, DLC gives you the same thing, but as Martimus said, DLC gives developers/publishers the ability to push out small pieces at a time, rather than having to wait for a full expansion release. It also enables players to pick and choose what they want a la carte, instead of being forced into a decision to purchase the whole expansion or not. In general, I don't think the cost of an expansion's worth of DLC is that much different than what an expansion would cost.
If anything, it provides more value to the consumer, because now I might choose to purchase a few new multiplayer maps for $10 because I exclusively play the multiplayer version of the game. They may offer a new episode for single player for $10 as well. As a person who is only interested in multiplayer, I'd rather be able to spend the $10 on the multiplayer maps and not have to pay for the single player content than be forced to spend $20+ on an expansion that includes content that I won't use.
I'm not sure that MW1 and MW2 would fall under the "would have been an expansion in the old days," either. While I never played MW1, I believe that MW2 had upgrades to the engine/features of the game in addition to basic content that would be in an expansion. It really isn't much different than looking at the GTA series -- Vice City added more than just a new map and missions to play. If you think that GTA is too recent, then you can go back to the days of Doom 1 and Doom 2 -- at first glance, Doom 2 was just new content, but if you really look into it, there were a lot of changes under the hood as well which made it deserve its title as a new game. If you want an even more egregious historical example, look at each year's release of the next EA sports game -- in general you get a very small engine/features upgrade -- the bulk of the draw of a new game is the updated roster.
The bottom line is that there isn't much difference between "then" and "now." The biggest change is that a portion of the "expansion" content has been converted into DLC where you can pick up stuff a la carte, and in general I don't think there is a big difference in cost.
I think the true gripe is not that DLC is replacing expansions, but rather that companies are skimping on content in the original game and splitting out the content into DLC. That is where my gripe with the system is, and is where I believe that the companies are looking to pull in more revenue at the expense of the consumer. The real question to ask is if today's DLC would have been included at no additional cost in yesterday's original release, and unfortunately I think the answer to that question is a resounding yes.
Before we all jump off the deep end, however, keep in mind that the cost of video games has remained fairly constant for 20 years. When you factor in inflation, the cost of a new game plus some DLC is still probably less expensive than a single game back in the late 80's or early 90's.