Daenerys Targaryen isn't just the rightful owner of the Iron Throne, she's the best suited for it
Everything that has been leading up to the final season of 'Game of Thrones' has indicated that not only is Daenerys Targaryen going to eventually sit on the Iron Throne, but she is also the most competent person to do so.
What do we look for in a leader? Someone who is compassionate, but strong-willed. A leader must have empathy to those in most need of it, and be merciless to those who would torment the same. More than that, a leader must be knowledgeable but accept advice when it has value. In all things, you look for someone who can inspire you to go beyond what you're capable of.
You can cite the theory that she is the Prince That Was Promised, her lineage from the House Targaryen, and her ability to ride dragons as her descendants did as reasons she should rule but what really makes Daenerys the rightful ruler is that she is simply the best candidate thanks to her virtues and her experience.
Since she assumed the mantle of Khaleesi and became the queen she was meant to be, her leadership style has pointed the way to her potential stewardship of Westeros. She has suffered great loss, known humility and shame, and has risen beyond these moments to become the leader we know. She's respected by her military leaders, feared by her enemies, and the violence's she meted out has been one as a liberator, not as a power-hungry despot.
The instances when she's used violence have been against those that she deems - according to her values - to be beyond saving. For example, the slavers of Meereen were crucified as a message to the cities of Yunkai and Astapor that their time was up. When Tyrion tried to negotiate with them in Daenerys' absence, they reneged on their promise to phase out slavery and ended up attacking Meereen instead. After she had the throats of the slavers who defied her cut and destroyed their armies, she picked up her dragons and her khalasar and left Meereen to be self-governed, having turned the city-state over to its own people.
That tells us that while she may be ruthlessly efficient against her enemies, she doesn't hold on to power for its own sake. A lesser leader would have stayed in Meereen, and ruled lavishly over the people and basked in the glow of their victory. Instead, Daenerys knew that she had done what she could for these people, and was destined to return home to do the same - namely, free Westeros from the rule of the Lannisters and the Baratheons.
When she arrived in Westeros in the seventh season and finally met with Jon Snow, the question of whether or not he would bend the knee took up most of their initial interactions. As Jon saw it, he couldn't bend the knee for two reasons - one, because the people of the North had chosen him as their leader and he took that duty seriously.
Secondly, whether he bent the knee or not was irrelevant, as stopping the Night King was the threat that faced all of Westeros, not just him. Again, a lesser leader would have simply killed Jon for daring to challenge them, taken control of his armies or put them to the sword, and carried on with their conquest.
Again, since Daenerys was able to listen to advice and accept that there's always a different solution than the most obvious one, Jon Snow not only joined forces with her (maybe a bit too much, in fact), the two are now in agreement on the common goal - defeating the Night King and holding off his forces by any means.
Whether she defeats the Night King and her former dragon Viserion remains to be seen, and the odds on her surviving are iffy at best, but one thing is clear - she has the skills, the temperament, the ability and the right to rule Westeros.