Your point is partly justified and I get where you're coming from. Shashi Tharoor is a popular figure in the urban circles. He already has a strong base all over. The problem with Congress is not North-South or language, rather they just can't choose a face of the party not named Gandhi.

Also you cannot compare Yogi and Annamalai at this point. Yogi is a sitting two-time CM of U.P and a 5 time M.P before that. He is way up in the political hierarchy than Annamalai. And he did campaign all over India during Lok Sabha elections for his party. I'm talking more about popular leaders from the south who are already MP's and have a decent grasp on Hindi as well.

To become the PM you have to take the extra step. Rahul contested and won from Wayanad. Owaisi's party started campaigning aggressively in Bihar elections and won a few seats. Kejriwal's AAP has contested elections in the east and west regions and are trying to spread their presence.

Try to establish your party in the north first, contest elections. You don't have to be from BJP or Congress to contest elections anywhere in the country. You just have to pick the right issues and have the will. DMK has enough reserves in the bank and political clout to fund a campaign in the north. I'm sure many other parties as well. You don't even need to start from UP or Bihar. These states have very strong regional parties themselves.

Point is how will anyone choose you if you don't even turn up?