Carl Edwards out, Kurt Busch in. That's my "line" and the two drivers I can think of that are closest.
Edit: it's case by case, and if your career in any way impresses the voting group then you 100% deserve a spot in the hall
This post gets 110% of my support.
Why?
Kurt Busch has nearly 30 Cup wins, including a Daytona 500 victory, a Coca-Cola 600 victory, and an All-Star Race victory. Last but certainly not least, Kurt Busch is a Cup champion, and he is also the first champion under the Chase format - I would think that he would be placed in the HoF by NASCAR for that alone.
If Carl Edwards had won a Cup title and a few more races, he would be a surefire candidate for the HoF, as well. Same goes for Denny Hamlin. His career is borderline as it is, right now. If he gets a Cup title, he certainly goes into the HoF. Pretty much anyone from Kurt Busch on upwards must certainly go in.
As far as Alan Kulwicki and Davey Allison go, I can certainly see why they made it in. Seems legitimate enough to me. They had the success combined with the fame, and Kulwicki pulled off a Cup title in basically what would be impossible circumstances in today's NASCAR.
Davey Allison, for as short as his career was, certainly had the ability to propel himself further and further up the winner's table. He never endured a winless season in his short Cup career, and his stats read like the stats from Kevin Harvick's tenure at Stewart-Haas Racing. Pretty impressive stuff.