Tyrion Lannister's too smart to sit on the Iron Throne, and that's exactly why he should
Let's be clear about this - there is almost no way that Tyrion Lannister is going to be sitting on the Iron Throne by the time 'Game of Thrones' ends.
Whether it ends up being Sansa, Cersei, Daenerys, the Night King or whoever - there is no way that Tyrion Lannister is going to end up on the Iron Throne. He's far too good, far too cunning, and far too clever to take on the duty of ruler of Westeros. And yet, it's because of this that he could be the best possible candidate for the position.
Consider the facts - Tyrion is, by far, the smartest character in the whole series. He's well-read and knowledgeable in warfare, commerce, diplomacy and cultures beyond his own. He is a skilled negotiator, an inspiring orator, and when it comes to it, a dedicated warrior and battlefield commander. He successfully led the defence of King's Landing, improved relations with the other Houses for his own, and was able to do all this in spite of the fact that most people treated him with contempt.
Whether it was his own father or other noblemen, Tyrion Lannister was able to take all of this on the chin, and stay the course that he deemed the best. As the son of the once-most powerful man in Westeros, Tyrion not only held his ground but counselled him in a better direction. When faced with certain death by Daenerys, he was able to skillfully move out of the firing line and into a vaunted position as chief advisor.
In all situations, Tyrion has been able to turn shit into gold and he's done it without ever seeking power for his own ends. That's not to say that he isn't aware of the power he wields, but never has it been so assiduously used.
What really sets Tyrion apart from anyone else in the running for the Iron Throne, however, is not his skills or his intelligence, or even that people underestimate him. It's that he's a realist and a pragmatist. In the last season, Tyrion knew full-well that the only way Westeros was going to survive the coming threat of the Night King was by suing for peace with Cersei and joining forces. More than any of them, he had a reason not to do it.
His family - well, except for Jaime - hated him. His father tried to kill him for a crime he didn't commit. His own sister, the one who he was negotiating with, tried to kill him at least twice. All of this, because he understood the implications of not doing it. That's a pragmatist. Someone who can set aside their own feelings in order to see something through to the end.
Jon Snow, for all his talk of honour and oaths, hasn't lived in the world very long. His principles are noble, sure, but Tyrion has seen the world and lived in it. He accepts it on its own terms and is willing to adapt to it in order to both survive and thrive. If you wanted a leader who was unwilling to bend, and incapable of seeing the world in greys and only in black and white, you're going to have a hard time living in it.
Tyrion, of all of the characters in 'Game of Thrones', accepts that the world is not black and white. People are complex, and while he's a complex person, he understands both the nuance and the challenges of what it takes to rule - and then specifically avoids it, because it's too much.
If the situation arose, and if there was no other way he could get around it, he'd be the best possible candidate for the Iron Throne.