I hate the whole "High King" thing, but it is arguable that out of all those Anduin (outside of maybe Turalyon) is the only one that has the diplomatic skills to actually lead all the Alliance factions.
Tyrande and Greymane are hotheads with their own concerns; Velen is a prophet, not a military leader, who until very recently was too busy thinking about prophecies to do pretty much anything else; Mekkatorque would rather tinker and barely wants to lead the gnomes, much less the entire Alliance; the Dwarves don't really have a singular leader at the moment (and if they did, it would be Moira, who doesn't exactly seem like she'd have a high Charisma score). The only human Alleria liked was Turalyon originally, and would probably prefer working independently as the Ranger she is than as Supreme Commander of disparate races, anyway.
Point being, there's more to being a "Supreme Commander" than just being a strong strategist. Eisenhower had to juggle Patton, Bradley, and Montgomery, for example, not to mention Roosevelt, Churchill, and (to some extent) Stalin. Say what you will about Anduin, that is something he'd be good at. For the most part. He might roll over a little too easily for Stalin and give in to his demand for a second front too early, but I digress.
Remember, the role of the "High King" is ostensibly to coordinate the independent forces of the Alliance, with their disparate ideas and priorities, and not to be dictator. This is assuming, of course, that "High King" is not just another "Warchief" (who is the supreme ruler of ALL the forces of the Horde) - a distinction I somehow doubt Blizzard is truly capable of making.
Interestingly enough, most of the Horde leaders (Thrall, Cairne, Vol'jin, Baine, Lor'themar, but not Gallywix, Ji, or Sylvanas) would probably make better "High Kings" than nearly any of the Alliance leaders.