If a team is a bottom six, shut down center, away from becoming a contender, then hell yes he's worth that first.
How many teams are in that position though?
The same amount who understand a "1st round pick" is really more of a glorified second round pick with where they'll likely finish and thusly will not scoff at the sticker price.
This board gets a lot of EA NHL Arm Chair GMing so the posters don't always understand what you're getting at. To them value is a number tied to a player, it's goals, or assists, or in some cases their draft rank. They struggle to see the whole picture as you mentioned, a good bottom 6 C is both an essential piece in building a Cup roster, and something that's not actually just growing on trees. I mean sure, you can plug any center into the bottom 6 role, but that's not actually going to yield results. Dowd has bottom 6 center skills that are desirable in the playoffs. He's a good two way player, his FO% is always around 50%, he is an asset on the PK, he hits, he'll fight, he is an above average bottom 6 passer, and he is an average bottom 6 shooter. When you consider how tight the playoffs become, you consider how stylistically the game changes when you play bottom 6 lines, it starts making sense why those player might fetch some value.
In the 2018 Cup run I would easily say the performances of Lars Eller (3C) and Jay Beagle (4C) would have been worth a late first round pick. We literally do not win a cup without both of those performances, that isn't necessarily maybe the case for the wingers on those lines, but those centers for sure were worth their weight.
And hell, maybe I just feel like that value doesn't seem crazy because I've literally seen this story before. Until the Capitals acquired Lars Eller (who was an absolute steal for two second round picks) the team always felt like they were that elusive 3C away from getting over the hump. What happened? They got their 3C and lost in 2017 to the eventual winners (IMO the '17 Caps were even better than '18), the next year they won the Cup. Same thing with Beagle, strong 4C, amazing PKer, fantastic FO%, really was the exact finishing touch needed on a championship roster.
The key here though is knowledge in your own roster. Jay Beagle never made sense in Van, they were not a Jay Beagle away from a Cup. So a guy like Jay Beagle (or in this case Nic Dowd) is maybe 100% worth a first round pick for some rosters, but most definitely not for others.