Byram certainly has some amazing stats... that's the one thing keeping me from losing my mind if we end up with him and everyone else throws a parade.
From what I have seen of his play, he's not that offensively talented (shot power, accuracy, stick handling, passing, speed all seem like nothing special). His points come from the fact that he plays like a 4th forward and is not a big fan of actually playing the defensive position. His pivot when skating backwards looks like he's in quicksand. His effort level seems questionable at best at times.
(Disclaimer: I am stating this opinion as a fan that looks at stats and does some youtube scouting. I am aware that my opinion comes from limited sources and I am no expert, but at the same time it is fun to have an opinion. I welcome with open arms any specific examples of what makes you a fan of his)
Don't worry, I have the same disclaimer (as should pretty much all of HF otherwise our lists would look way less consensus).
Honestly you're not wrong that Byram lacks an elite flashy skill that really stands out (his sksting is almost there). Furthermore he is super willing to jump into the rush and that's risky sometimes. But I think you're underrating each of his skills individually, especially his skating and vision/IQ. He's good at everything, he's nearly elite there.
Whenever I watched an actual game with Byram two things really stood out to me, how often he has the puck creating offense and how rarely he gets burned because of it (he definitely does get burned sometimes though). And I attribute that to those two things, his skating and smarts.
He sees the ice well enough to find the right lanes to take and skates well enough that he can hit them without having to make a flashy play. When he does lose the puck carrying it he gets back well and usually recovers. He's aggressive because he can do that. Add that his hands are good enough to beat guys when they challenge him, his passing is good enough to set up teammates and he has a good wrister that he gets through (it's pretty hard and he is dangerous to pick a corner when he moves down) and to me, he's a complete package offensively with his skating and vision being the foundations of his game. I love defenseman that skate well.
I also think he's the odd young offensive D that's actually really solid defensively. I haven't noticed his pivot looking slow backwards and I really like the way he uses his body and positioning to angle guys to the outside. He never gets beat clean by a forward. If they rush him, they get pushed to the outside. If they dump it, he's always there first and the puck is going the other way. Turn it over to him and he's flying down the ice with the puck leading the rush. If you want to score when Byram's on the ice you have three options IMO: score off the rush when he's behind your net (you better be fast because he's coming), completely outmuscle him in the slot and get a dirty one (you better be big because he's not small), avoid him and try to rush the other side of the ice (you better hope his partner is sub-par). Otherwise your rush is turning into his going the other way.
If I could design a D, he would be Byram with a flavor of Boqvist. If Byram had slightly better instincts in the offensive zone- sometimes he can get caught in a cycle of just making safe plays repeatedly, short passes, shots for rebounds when nothing is presenting- and a better shot (both slapper and wrister though as I said his wrister is quite good), he'd be my perfect D really (assuming you can't just ask for someone that's elite at everything, 7' and unstoppable).