No, absolutely not. Twilight Princess fully tied up its own story and left little to no room for expansion. When you try to expand on a story that concludes itself, what you end up doing is damaging the integrity of the original story. The worst example of this is the Mega Man X series, which was intended to end with X5, and had it done so, it would have segued into the Mega Man Zero games perfectly and told an amazing story. Expanding onto X5 with three more games essentially broke the continuity and turned it into something far less interesting. Even if X6 had been the only sequel, it was pretty much the worst offender.
Bottom line is, trying to expand on something that doesn't need expansion is a mistake, especially for the sake of the original. Zelda's never been a series that prides itself on continuity in any serious way, so there's no reason for it to start.
I do! I think Nintendo left a lot of room to continue the story after TP, and also to give more substance to TP Zelda's character, and relationship with Link. I think there's a good chance that Nintendo will make a sequel, given how they ended TP with link riding out of Ordon.
Nearly every Zelda game has an ending that leaves an opening for a new adventure. It's a stereotypical way to end off
any story, and you'll see it everywhere. It doesn't indicate that there's any serious room for expansion, nor that expansion could be in any way benevolent. As for Link and Zelda's relationship... you should know that Nintendo never seriously elaborates upon nor finalizes any serious relationship between Link and Zelda. Expecting them to do that in a sequel is hopeless.
So aside from that, how did Nintendo leave any room to continue the story? The stories of Midna, Zant, Ganon, King Bulblin, Ilia, the Ordon villagers, and yeah, even Link, have basically concluded. There aren't any themes in TP left to expand on.