I think the biggest factor in choosing who to represent the Knights Radiant is that there is a huge war on. The coming Desolation is on scale beyond anything that anyone living (sans the heralds) has ever experienced. Dalinar is renowned across Roshar as the unstoppable warrior known as the Blackthorn and respected as the most honorable of the Alethi Highprinces. Only a small tenth of a percent of the population will ever interact with Dalinar in any significant way. For the vast, vast majority he will simply be the leader of the Knights Radiant and the de facto ruler of Alethkar, the world's most powerful Kingdom. For them, Dalinar is most important as a symbol, they have to believe in him and the Knights who have scorned as traitors for thousands of years. They have to believe he is capable and willing to protect them. With his reputation as a general, warrior and honorable man, Dalinar is the best person for the job.
As for the people who will interact with him, the Highprinces and lesser nobles of Alethkar respect his martial power, and will likely be a bit in awe of him after this latest battle and transformation. He's proved his visions are real. Sadeas has conveniently died. None of them are likely to openly oppose him for some time. As for Kings and nobles from elsewhere, they will know his reputation generaly, and their view of him will greatly increase once the Everstorm has circled the world once. He should be able to work with them.