TBH WC lore has never been good with dealing with the 'teleportation' mechanic that the more powerful (Arch)mages can employ.
At least in some instances they try to indicate that it requires and consumes a healthy chunk of the mage's reserves, hence it's not used constantly, particularly in combat.
It'd also be reasonable to assume that they employ certain anti-teleportation magics in certain instances, i.e. you wouldn't want mages to be able to teleport directly into a throne room unannounced, now would we? I would expect most parts of Capitol cities to employ magic/mystic defenses, particularly in Castles/Thrones Rooms etc etc, esp Stormwind+Org. Admittedly this doesn't explain why he didn't teleport to the Mage's Enclave or w/e it's called, as this area is obviously 'unlocked' for this purpose.
Let's be honest - in real terms Khadgar would have used magic to communicate with both Dalaran and The King @ Stormwind immediately following discovering the Burning Legion's presence, as there would already be mechanisms in place for this type of alert. Or at least there sure as hell should be following the events of the last ten years!