Here's the NFL Throwback list:
Wilson
Largent
Jones
Wagner
Now, my TL;DR version:
Largent
Jones
Kam
Tez
VL;WR (very long; worth-reading) version:
I think it's important that the question is the *Mount Rushmore* of Hawks, not the best Hawks. If we're just going for the best Hawks, then the HOFers (Largent, Jones, Easley, Tez) would be a good choice.
But the Mount Rushmore of Hawks should be about which players defined important eras because that's what Mount Rushmore is all about:
Gutzon Borglum selected these four presidents because from his perspective, they represented the most important events in the history of the United States.
So, with that in mind, my Rushmore has two easy selections:
1. Largent. He was our first HOFer and was, IMO, the most iconic Hawk from the first era of the franchise. I think Easley was a much better player, but for most Hawk fans, Largent is the face of the 80s teams. His hit on Harden is legend, he broke the decades-long TD record, etc. He was great, he gave us moments, and he was loyal for his career.
2. Jones. The Holmgren years brought us our first SB appearance and his teams were all about the offense. The fact that the best player in Hawks history played in our first SB and on the side of the line that defined that team makes him an easy choice.
Now it gets tough, because we need a representative of the next most important team (chronologically), the SB-winning team. That team has to have a member of the LOB because the LOB defined that team. I think you could make a good argument for Wags here because he's the only surefire HOF player from that defense. And if you think of him being part of the "LOB defense" then that makes sense. But I always think that the LOB = Kam, ETIII, and Sherm, so for me it has to be one of those guys. I think ETIII was the most important player in terms of scheme because Pete's defense doesn't work without him. But he was never a representative for that defense. Plus, with how he left, there's no way in hell he gets up there. Sherm was the best known face/voice and has The Tip and the interview after that, and he has a marginal HOF case, so you could go with him and I wouldn't argue. But I'm going with...
3. Kam. He was the soul of that defense, the reason the LOB was feared. And he had the most iconic moment of the biggest game of Hawks history. When he laid out Thomas (like Vernon Davis before him) I had no doubt the Hawks would win. He'll never get into the HOF, but the Mount Rushmore isn't about our best players. It's the era-defining ones, and I'll take Kam.
The fourth one is also tough, because I'm not sure there is a fourth important era of Hawks teams. What other team was good enough to demand a representative? None, IMO. We could go with Paul Allen, because he saved the team. But an owner is weird on this, to me at least. You could go with Pete, because obviously, but I would rather have just players. Personal preference and I wouldn't argue with others who are okay with non-players. We could point to the SB-winning team and say we need a second representative because the win is the most important moment in Hawks history, and then you can go with Wags (most likely HOFer), Wilson (most important position), or BeastMode (he was the first player to give the Hawks an identity as a physical team, plus he's my favorite Hawk because he's just awesome). But I think that team doesn't need a second rep. That's why I'd have the fourth face be...
4. Tez. There is nothing about this team or era worth memorializing, but I think he's the second-best Hawk of all time (barely nudging Easley because there are fewer elite DTs than safeties), and he's from a different era than we already have.
We've now got each of the four decades (roughly) represented. Two offense, two defense, different personalities, different positions. This feels well-rounded, respectful of history, and true to the team I've loved watching for 40 years.