So if you're "doubting we're going to see that much improvement", why are you panicking about paying him sooner? That's a contradiction.
Trent Dilfer won a Super Bowl too, as did Brad Johnson. That's on their "resumes" as well. But that doesn't mean that they were good, it just means that they were on great teams that carried them.
I'll present the exact opposite reasoning. This team isn't in the Super Bowl, but you rushed to pay the quarterback. Now you're stuck, your coach was fired for not reaching the Super Bowl, and you now need to find a coach willing to sign on to coach a grossly overpaid quarterback. You yourself said "I doubt we're going to see that much improvement from Dak waiting another year."
While I don't deny that all of these played a role, it's also undeniable that the quarterbacking did as well.
Couple points here and this just my take.....
The whole theory of a team carrying QB or he needs weapons around him is simple BS IMO. NO QB not named Brady can win this league w/o combination of weapons, coaching or great defense. I challenge any fan to show a winning Super Bowl QB that didn't have at least 2 of these combinations. Example.....look no further than the final four teams NFL championship games.
Ram....loaded with talent on both side of the ball
Saints...see Rams and Peyton
Chiefs ....Ford, Houston, Hunt, Hill, and Reid
Pats.......Brady and Belichick says it all
Wanna hear something funny, over the last 3 years the majority, if not most fans have wanted both Garrett and Linehan fired but the Cowboys have won anyway, even making the playoffs 2 out 3 years. Who gets credit for that? (Bad coach AND QB) Either Dak is pretty darn good ( winning with TWO bad coaches ), Garrett and Linehan were not as bad as some fans wanted you to believe, or many fans are misguided by personal emotions/agendas coz you can't have it both ways. Hell, bad QB with bad coaches yet you still winning AND making the playoffs. How many fans we never hear say one word about the top talent most so-called elite QBs are surrounded with but Dak can't win w/o it. Again this is just my take, but I care about one thing WINNING. As long as we're doing that, someone (coaches, players, FO ) is doing there job. We as fans may not like the way it's being done or sexy enough but it's getting done.
With regard to "doubting Dak would improve"......it's doubting you're going to see that much improvement in a year ( timeline of waiting to extend ). It's why I said we could see a slight bump in his stats from 2018 -2019.