This has nothing to do with presence in WoW. Let's get things straight - I'm talking about mainstream recognizability and familiarity to the Warcraft franchise. Anyone and everyone knows what a Demon Hunter is, because Illidan has been explicitly in the forefront of the lore, the cinematics, and everything else. His presence has solidified the Demon Hunter's place in Warcraft. Same can be said of what Arthas has done for Death Knights. People know what Death Knights are over a Runemaster any day. Demon Hunters are recognizable to the franchise to the point of having been asked for by a wide variety of fans, both enthusiast and casual player. Tinkers simply don't have this sort of presence, and the association to Gnome/Goblin exclusivity will only hurt this new class impression. Keep in mind, I'm not talking about the Tinker specific identity, rather I am speaking out for a broader 'Tech/Engineering' themes which already exists within WoW and has much broader application than simply Gnomes and Goblins.
Gnomes and Goblins don't make a good first impression. In fact, they are one of the races most spoken out against (along with Pandaren). This invariably hurts the image of the broad 'New Tech-based class' due to its limited offer in race choice, especially in the wake of other races which we've already talked about.
While I can easily say that Blizzard's choice of Demon Hunter doesn't benefit the game in terms of varied themes and gameplay, it does work to promote players coming back to WoW to play as one. The Demon Hunter is just one of the few marketting tricks Blizzard is using to bring interest back into WoW. They've set the stage for a Demon invasion, they introduce a highly sought-out class that is immediately familiar and recognizable, and because of its popularity they can design the class to be as exclusive/limited as they wish. The Demon Hunter sells itself, and carries the expansion on its back.
Now let's say instead of the Demon Hunter, they introduced a Bard class instead. Would Legion still have the same strong impact as it does now? Would having a Bard-centric expansion work its same magic as Legion and the Demon Hunters? Do Bards make a strong first impression? Bottom line is that new classes are a marketting tool to keep an aging MMO fresh. It gets people talking, and word of mouth for awesome new shit is what ends up bringing me, you and the entire guild back to WoW.
If Gnomes and Goblins had that impact for WoW, I'd be in total agreement with you that we should have exclusive Tinkers. But simply said, they don't. The Tinker class has potential, but being restricted to unpopular classes will ultimately doom it into obscurity.