It's a fair point, but the fact is that it's never in the same year, and the teams that have won multiple cups in that time span, have had a 1st overall. So in this hypothetical, you aren't even getting a 1st overall pick. So really you would need a president's trophy win AND a first overall pick. If you have won 2 president's trophys over a 5 year span, that chances that you're drafting high enough to obtain that pick are extremely low.
Also, you're forgetting Ovechkin - 2018.
Who cares about the first pick when you are guaranteed a 2-9 year window of contention? The Presidents' Trophy winner only wins the Cup
8 out of 35 times in the same year the team wins the Presidents' Trophy. But if you extend the range to include either the 4 years before or 4 years after winning the Trophy,
24 out of 33 Presidents' Trophy winners have eventually won the Stanley Cup while they were still in their window of contention. Nashville 2018 and Boston 2020 still have a few years of wait-and-see, but even then both of those teams had made the Stanley Cup finals at some point in the window around their Presidents' Trophy season. If we narrow the range down to teams that won 2 Presidents' Trophies in a 5 year span,
8 out of 9 teams that won Presidents' Trophies twice in a span of 5 years have won Stanley Cups, and the lone team that didn't (Vancouver 2011 and 2012) made it to Game 7 of the Cup finals.
On the flip side,
since 1985-86 (the first year the Presidents' Trophy was awarded)
only 7 1st overall picks have gone on to win the Stanley Cup while playing for the team that drafted them at any point in their entire career. That's even less than the number of teams that won a Presidents' Trophy and a Stanley Cup in the same year. Those 7 players (Mike Modano, Vincent Lecavalier, Marc-Andre Fleury, Alex Ovechkin, Sidney Crosby, Patrick Kane, and Steven Stamkos) are also the only 1st overall selections to have even made it to the Stanley Cup finals with their original team, unless you want to include Eric Lindros (whose selection and subsequent trade led to the Avs winning a Cup twice and the Flyers making it to the Finals once).
I'll take a 100% chance of making it to the Championship round and an 89% chance of winning at least 1 title over a 1st overall pick any day. Being the best regular season team in the league guarantees you a chance. Doing it twice means it's not a fluke, and ensures you are going to be a contender for a 5-9 year window. Obviously currently contending teams would love to take the player and poor teams would rather take the guaranteed opportunity, but in a nutshell ignoring teams and starting a franchise from scratch with a magic wish granting genie there's no way I prioritize the 1st overall pick over guaranteed success and contention.