Warning : This blog contains spoilers from the books.

"If Stannis Baratheon becomes the king of Westeros, what good will it bring to the realm?"

Stannis Baratheon falls into the category of what we may call a 'grey character.' He's not a prince charming neither is he some good disney king. He is a survivor and survivors have to learn the harsh realities of life to avoid getting perished. He has seen the ups and downs of life, he suffered the hardships of fate without becoming some vile creature. He still desperately tries to hold on to his ideals and principles.
Donal Noye said,

“Robert was the true steel. Stannis is pure iron, black and hard and strong, yes, but brittle, the way iron gets. He'll break before he bends. And Renly, that one, he's copper, bright and shiny, pretty to look at but not worth all that much at the end of the day.”

But Stannis has bent in order to avoid getting broken. He has turned to magical powers & broken his personal code of conduct, lately. He is no longer that blotless honourable man as he once was. 

WHY IS STANNIS THE NEED OF HOUR?
The greatest danger to seven kingdoms is in the North, a horde of white walkers is bent on crossing the wall to ravage Westeros. 
Aegon VI has showed up out of nowhere; the court is full of self serving snakes. Eventually 
Daenerys Targaryen may launch an invasion to claim the throne. The North has not fully sworn fealty to the new Wardens of the North(Boltons). Freys are not very popular in Riverrun either. Petyr Baelish holds the strings in the Vale. Greyjoys under the restless Euron have increased their raids.

So, what Stannis has to offer in these turbulent times ?

1) He was the only king who responded to the call from the wall. He was the one who realised that the real danger lies North of the Wall. He acted selflessly and sailed with his army to a threatening place. In doing so, he did not fight for any crown or glory, he did what a responsible king should do.  

"Few of the birds that Maester Aemon had sent off had returned as yet. One reached Stannis, though. One found Dragonstone, and a king who still cared."(Samwell Tarly)

2) This man ate rats and dogs while defending Storm's End during Robert's Rebellion. The Siege lasted for one year. Stannis held against the might of the Reach with 500 men. This proves his resolve & loyalty. He out survived the other four kings during The War of Five Kings. He has the will power to go the distance. A long winter is coming and he can withstand the threats to the realm.

"This is Stannis Baratheon. The man will fight to the bitter end and then some."(Tywin Lannister)

3) He is a proven battle commander, apart from Storm's End, he captured Dragonstone & destroyed the Greyjoy fleet during the Greyjoy Rebellion.
He defeated the army of the King Beyond the Wall, north of the wall, in Mance Rayder's own backyard.

"I defeated your uncle Victarion and his Iron Fleet off Fair Isle, the first time your father crowned himself. I held Storm's End against the power of the Reach for a year, and took Dragonstone from the Targaryens. I smashed Mance Rayder at the Wall, though he had twenty times my numbers. Tell me, turn cloak, what battles has the Bastard of Bolton ever won that I should fear him?"(Stannis to Theon Greyjoy)

Although he got defeated in the Battle of Blackwater Bay but the odds were too much stacked against him. He had attacked King's Landing with around 20,000 men, lost most of them by the time Tywin and Loras arrived with a reinforcement of almost 80,000 men.

4) He has a reasonable support base in the North. If he wins the Battle of Winterfell, then he would gain much favour amongst some major houses in the North. He has earned himself a good reputation by protecting the Night Watch against the wildling onslaught. He also has Theon Greyjoy in captivity, who is still believed, by many, to have killed Bran and Rickon.

5) He believes in meritocracy, in such crisis what the crown really needs is men of merit to steer the ship through the stormy days that lie ahead. He is not a tyrant when it comes to decision making. He listens to the opinions of his advisers.

6) We all know how 'King' Joffrey behaved when Stannis' invasion force knocked at the doors of King's Landing. Tommen is a boy with no experience in the field. With Tywin and Tyrion no longer there, we cannot have much high hopes from Tommen.

7) He is the rightful King of Westeros by law. If peace is to prevail then laws must be adhered to and laws are expected to be implemented by a king who is just and not a usurper.

8) The Iron Bank of Braavos lent huge sums of money to the crown. Now they are backing Stannis because, being a man of his word, he can ensure the return of their investment. In case the money is not paid back, the Iron Bank may as well use 'punitive means' against the Seven Kingdoms.

There are many other reasons that make Stannis a strong candidate for kingship but being a mortal man, he also has many flaws. However, considering the current scenario, I would like to see Stannis sit the Iron Throne. The Stag on Fire is the ray of hope for Westeros in such dark days.

In the words of George R.R.Martin,

"The real issue lies in the North beyond the Wall. Stannis becomes one of the few characters fully to understand that, which is why in spite of everything he is a righteous man."