I'm not as concerned about what guys do on offense as much as whether they are competent guarding opposing point guards. Offensively there are any number of guys who have the ball handling and passing skills to be a traditional point guard, whether it's Francisco Garcia, John Salmons, or heck, Brad Miller. The reason those guys can't function playing the one is that they can't hope to keep up with opposing point guards, and they're not quick enough to bring the ball up the floor against quick point guard who are good defenders.
I don't think Tyreke Evans is quick enough to play the point. He's quick for 6'5", he's not quick compared to the 6'1"-6'3" point guards in the league. I think he'd struggle to bring the ball up against good defending point guards, and he couldn't hope to guard them at the other end. I could be proven wrong on that, but I think he's much better suited to be a ballhandling 2 guard, a la Brandon Roy.
Meanwhile, Teague is plenty quick enough. Everyone's beef with him is whether he's a "pure" point guard, which is completely beside the point. He's a point guard, whether or not he's best suited trying to pass or trying to score. He can't guard shooting guards. If he's going to succeed in the NBA it will be probably be as a scoring point guard, but people around here are overly fixated on traditional point guard skills anyway.
Semantic battle ahead. . .
Addressing the first bolded: That preference is certainly your prerogative, but I don't think defensive ability is relevant in defining whether a player is a point guard or not. It may or may not be relevant in deciding if a guy is an NBA player, but not if they are or are not point guards. For example, Kobe Bryant or John Salmons may be able to defend the point better than a Steve Nash or Mike Bibby--arguably both also have a stronger handle than Bibby who had on occasion trouble advancing the ball against quicker points--but few would label Salmons or Bryant point guards. Perhaps Magic Johnson would be a Nash level defensive player in the modern NBA due to the better athleticism of the current players, as well as the rule changes that favor the offense. Would people consequently claim Magic was no longer a point guard? I think not. The qualities that most define the word "point guard" must therefore be different.
I don't think it is accurate to make it a binary choice between "pure point guards" and "scoring point guards, where the latter category wraps up everyone from Mike Bibby to Steve Kerr; such a classification is too broad and makes the term muddled to the point of uselessness. A better system (I think something like the following has been written more than once elsewhere) for player classification is needed to paint a more accurate picture.
Say we did a 1 to five scale: 5's would be the pure points who are pass first, pass second, score only when absolutely necessary. John Stockton, Jason Kidd, etc.
4's would be those rare talents that legitimately excel in both abilities: Paul, Deron Williams, Steve Nash, etc
3's would be guys who are at least competent play makers, but may excel or be below average as scorers: Bibby, Steph Curry, Jameer Nelson, etc. This would be the final category I would classify as point guards.
2's are Combo guards-- guys who have a scorers mentality and possess some limited play making ability; though not enough ability to be legitimate point guards: Bobby Jackson, Aaron Brooks, Mo Williams.
1's Mini shooting guards--guys who shoot first, second; and pass begrudgingly when a gun is pointed at their heads: Eddie House, Quincey Douby, Jeff Teague.
I do agree with you that it isn't necessary to possess a pure point in order to field a winning team; however, I think if Jeff Teague is manning the position for us then we would need a player more resembling an Eric Snow or Doug Christie at the two rather than a Kevin Martin.