I guess one flaw with my fantasy of a Doctor Who MMO universe is that MMOs are typically centered around combat. Doctor Who, on the other hand, was usually non-violent. It was rare to see the Doctor pick up a weapon.
I guess the obvious solution would be to militarize the game in some fashion. Since you obviously can't play the Doctor anyway, players could belong to a Time Agency or some other group alluded to in the series, who wage war across time against various time travelling enemies hell bent on conquering history. Captain Jack Harkness did carry a sonic blaster instead of a sonic screwdriver after all.
Star Trek was usually non-violent too, but Perpetual seems to have taken the obvious approach of making Star Trek Online more militaristic.
Are there alternate means of providing obstacles to players that can be explored in an MMO? We've seen diplomacy in Vanguard (kind of...). That was somewhat of an card game. Would an MMO that used puzzles or card games to simulate "defeating an obstacle" interest players?
Could a game be done in a way that doesn't use loot as a means of advancement? The Doctor was rarely seen collecting anything except celery sticks and jelly babies. But, on the other hand, I don't recall Luke Skywalker upgrading his armor after a battle with the Stormtroopers either, and the current post-NGE Star Wars MMO is pretty darn loot-centric.
Doctor Who would definitely work as a single player game, and it appears that I'll at least get that part of my wish. They are going to release a Doctor Who video game this Christmas!
I would still love to see Doctor Who as an MMO, but it would require some creative thinking to present it properly.