I follow your train of thought, but I just think you've set the bar very high with finishing top-two in their division AND winning at least two rounds in the playoffs more often than not.
I looked at the most recent Stanley Cup champions pre-cup records as follows:
St. Louis won the Cup in 2018-19, finishing second in their division that year. Previously, they finished second and won two rounds in 2015-16, and haven't done that before or since 2009-10 when I began my search. In 2017-18 they finished fifth in their division and missed the playoffs. In 2016-17 they finished third and won the first round and lost in the second. From 2012-13 to 2014-15 they finished first or second and lost in the first round three straight years. Probably lots of gnashing of teeth, as they didn't come close to your true contender status.
Washington won the Cup in 2017-18, having finished first in their division. Prior to that, I don't think they had ever advanced beyond the second round of the playoffs -- and certainly not since 2009-10. No luck there. They weren't your true contenders either.
Pittsburgh won back-to-back Cups in 2015-16 and 2016-17, finishing second in their division each year. Prior to that, going back to 2009-10, they met your standard only once, in 2012-13 when they finished first in their division and lost in the third round - Conference Finals. In between that year and their Cup championships, in 2014-15 they finished fourth and lost in the first round; and in 2013-14 finished first and lost in the second round. Before that they finished first or second three years in a row, and lost in the second round once and the first round twice. Closer, but no cigar.
Chicago I think does come pretty close to meeting your definition of a true contender from their Cup championships from 2009-10 through their later Cup championships in 2012-13 and 2014-15. In between their last two Cups, they finished third and lost in the third round in 2013-14; and in 2010-11 and 2011-12 finished third or fourth in their division and lost both times in the first round. Their three Cup championships and one Conference Finals loss in six years definitely makes them a contender, but even at that the only seasons they actually met your very high criteria were their actual Cup championship years -- but three in six does it every time.
Now were getting more dated with LA, Boston, and I looked at Tampa even though they don't have a Cup within the past 10 years. None of them meet your standards.
Boston met the mark three times -- in 2018-19 they finished second in their division and lost in the Stanley Cup finals; in 2012-13 they finished second and lost in the Cup finals; and in 2010-11 they finished first and won the Stanley Cup. Very impressive, but in the five years from 2013-14 to 2017-18 they missed the playoffs twice, finished fourth twice, second once and first once; and lost in the first round once and the second round twice in the years they did make the playoffs. They have won two rounds three times in the past ten years, and don't meet your standards of a true contender.
I think you get the drift and there's no need to continue. Chicago comes the closest, and none others reach the bar.
I understand what you mean, but I think that what you meant is probably not exactly what you said.
I would also say that pretty much every team that wins the Stanley Cup has its' own tale of repeated disappointments before that, and it's not at all unusual for success to follow repeated failures.
If and when the Leafs win it will be no different for them.
Marner is certainly not better in the playoffs.
