Mean something? Of course it means something. We're talking about it, which alone is proof that it's one of those stats out there that serve as indicators of the long-term success of a program over decades. # of wins all-time ... # of bowls and bowl wins all-time ... # of NFL players all-time ... # of years with an NFL draftee ... etc.
There are small "clubs" of teams at the top end of each of those lists. Tennessee is in most of them. But we just got shown the door on this one, and--unfortunately--it's one you can never get back into once you're out. That's the real pity of the streak getting broken.
Plus, this is one of those markers you can put down on the coffee table in that 5* high school recruit's living room. Want to get to the NFL, son? We've sent players there every single year ... only six teams in all of College football can say that. Oops. We can't say that any more.
It's not a catastrophe, we still have a ton of other positive selling points in recruiting, and other laurels to show that we're one of the all-time elite programs in the nation. But each time we lose one of those, it's painful. As it should be.
That's why it means something.