True, but remember that Tevinter also boasts a supposedly meritocratic stance. Pure lip service in practice, as Fenris and Dorian pointed out, but they like to sell the idea that anyone can become powerful. Like how in theory non-mages can be Magisters, and probably the same could be said about the Archon.
The thing is, Tevinter is going to be in a very delicate situation in the next game, with the Qunari invading. Roman and Byzantine history is full of examples in which military leaders from the lowest origins could rise to the imperial throne in times of crisis. That could be used it here too.
Also, if it is a non-mage, it could be a reverse mirror of what happened in the past. Although the separation of the Black and White Chantries in 3:87 is considered sometimes the beginning of mages controlling Tevinter politics again, in reality it wasn't until the election of Nomaran as Archon in 7:34 that restrictions against mages in politics were lifted. The process to return the country to a full-fledged magocracy ended around 8:11 (yes, despite common perception, the current oppressive magocratic rule is fairly recent), and the timing conveniently coincides with the last (and greatest) push in the Qunari Wars. It's not hard to imagine that the menace of the Qun made Tevinters embrace magocracy as the solution. The opposite could happen for similar reasons.
Magic, when not nerfed by gameplay reasons, is a true storybreaker power in Thedas.
Corypheus, after losing the political and military means to control the world, resorted to ancient magic in the hopes of crushing the world afoot with it and for all intents and purposes it could have worked.
Solas changed the very fabric of reality when he created the Veil, by far and large the greatest magical feat of all time, so a sufficiently powerful and knowledgeable mage can bend the entire world to his will.
On topic, when the Qunari invaded, the regular forces of Tevinter were minced meat against a numerically and technologically superior faction and they got their assess kicked until only Minrathous was left unconquered.
Desperate to turn the tides they basically removed the limiter on their greatest resource, a bucket load of extremely talented mages. Unsurprisingly, the mages did what they do best and blew up the Qunari army back to the sea.
However, once you give someone greater freedoms, it's basically impossible to take those away without major violence. Since the mages had become celebrities who could wreck major havoc if attacked and the government was too weakened to reign them in, they basically seized power in a country which their influence was no longer kept in check.
Not only this change allowed the Imperium to survive but it also began reverting their decline, as mages became more powerful, so did the imperial military and new and more powerful magics began to be researched again such as Time Magic.
Fenris stated that despite being a far match from the Qunari in terms of raw military power, the Imperium had recovered a significant portion of their power and influence to the point they threatened all other nations of Thedas.
Indeed, the Venatori, despite being a terrorist organization not officially endorsed by the government and the regular military, had enough strenght and numbers to fight the entire Orlesian army when combined with either the Southern mages or the Red Lyrium Templars.
The only reason the Imperium was thrown into chaos is because Solas, who is basically a physical god, freed a huge portion of it's slaves thus wrecking the economy which was followed by an all out Qunari invasion.
If it wasn't for Solas, Tevinter would have easily returned to full power in a century and put the entire world in check with a massive army of mages.
Anyhow, that's why the next protagonist comes from Tevinter, he or she will become either the redeemer of the bastion of human civilization or the tyrant whose armies will bring the imperium to a new age of supremacy.
By far and large, don't expect any option to support the Qunari, Bioware made it abundantly clear that they will be antagonistic in the next games and they certainly don't have the time or the patience to write a divergent story in which the Qun wins.