The basic principle of a MMORPG is that the player has access to a virtual world which offers very different activities for him. He can quest, he can farm monsters, he can socialize, he can PvP under different rulesets (battlegrounds, arenas, open world), he can engage in cooperative PvE in different group sizes and difficulties (dungeons, heroics, raids), he can gather resources, he can craft items, or he could just travel the virtual world as a tourist. Offering so many different things can be attractive, but it also has disadvantages: It is expensive to produce, and invariably some activities end up being much more popular than others; sometimes the various activities even hinder each other, for example the spell the developers would like to put in for PvE would unbalance PvP, or the ability to craft really good items would keep people from searching for loot in dungeons.
After many companies failed miserably at offering a popular MMORPG which has something for everybody, the game flavor of the day isn't the MMORPG any more, but the MOBA (multiplayer online battle arena), the lobby-based game of PvP in instanced battle arenas. There are various games like these based on the DotA real-time strategy / role-playing mix. There are many different shooter games; including World of Tanks and the other announced "World of" games, which is somewhat ironic because their main difference to a MMORPG is the absence of a world. As much as Trion claims that their MMORPG Rift is successful, their next game is a MOBA: End of Nations, a real-time strategy, lobby-based game. Even the ancient Age of Empires brand this week opened up Age of Empires Online, which also is a MOBA. And Mythic re-designed their failed MMORPG WAR as a MOBA too. Pretty much all of these are based on the Free2Play business model. And unlike the MMORPG business which has 10 failures for every successful game, most of the MOBAs appear to be making money. Lobby-based games concentrating on just one activity are obviously cheaper to make than MMORPGs, without being any less popular.
Many fans of the world aspects of MMORPGs already complain that tools like the Dungeon Finder enable players to run dungeons as if they were in a lobby-based game. Only that this creates an extremely expensive and badly balanced lobby-based game. The MOBAs are frequently PvP games, but for example Age of Empires Online also has an extensive PvE campaign. There is no reason why we couldn't have MODs (multiplayer online dungeons) or even MORs (multiplayer online raids). Judging by how the people who play dungeons and raids always complain about having to play the leveling game, or doing quests, or doing other activities to get consumables for raiding, it is quite likely that a lobby-based game with dungeons and/or raids would be extremely successful. Not to mention much cheaper to produce, and much better balanced. And on the other side of the equation we could have MMORPGs with better virtual worlds, more meaningful questing and leveling, without that annoying raid endgame tacked on the end. Make two games for the price of one, each one better than the compromise you get by bundling them together.