The Rangers weren't rebuilding from 97 to 04 though. They were mucking things up without a coherent direction.
I'm again going to take issue with your characterization of it being unacceptable. You haven't explained WHY it's unacceptable.
Just because other teams have turned things around quickly doesn't mean it's the way for the Rangers to go.
This is why missing the playoffs a fourth year shouldn't be unacceptable:
1) Long term dynasty build should be the goal of this organization right now. There is no other acceptable goal in my book. Do you disagree?
2) One of the strengths of this organization is being a financial powerhouse and there is no evidence that the profit margins are down significantly enough to effect our status as financial powerhouse in the league (maybe some execs feel that pressure, but I'm arguing, they SHOULDN'T, since again, the profits are still there and they will be made up for by being a long term winner).
3) Another strength of this organization is it's attractiveness as a destination (for most players) and also as a class-A well run organization that treats its players right. Neither of those things are in jeopardy from 4 straight missed playoffs.
4) There is no proof that missing the playoffs 4 straight years effects player development long-term (especially since many of the players who will be team cornerstones were not on the NHL roster in years 1, 2 or 3, but instead were in minor leagues, overseas, or were undrafted at that time).
5) Conversely, there IS a strong correlation between not acquiring enough high-end talent in the draft, and failing to win a Stanley Cup. Teams with multiple superstars win more than teams without. This team has seen that happen just in it's last era: Very good, but lacking one or two more stars to get them over the hump, to get that key goal when they needed it. You could say this possibly cost them THREE Stanley Cups from 2012-2016.
6) And finally, we are fresh off an extended run of deep playoff success. This isn't, say, the 2006-07 Rangers who flirted with missing the playoffs, who, after the 97-04 drought, made the playoffs in 05-06. That team, you could say, hey, it's unacceptable that this team misses the playoffs. It has to build towards something after making the playoffs last year. It can't slip back to it's 7-year dry spell. But this team isn't that. This team is fresh off a 7 year era of deep playoff runs. This team has that good-will still built up. It's fans understand that. It's fans don't want to see a repeat of 10-11 to 16-17, where it was always "close but no cigar." It wants to see a Champion.
What's the best way to build a champion? See above.
That's why some patience on missing the playoffs a fourth time is not unacceptable. Not yet.
Maybe at 6 years it would become unacceptable. Because then you would have to conclude the talent acquisition is failing (ie, if a 22 year old Kakko and a 23 year old Kravtsov and a 24 year old Chytil and a 27 year old Shersterkin can't carry this team to the playoffs, then there's something wrong). But 4 years? With 19 year old Kakko and 20 year old Kravtsov? Nah. That's perfectly acceptable.