Why Ottawa?
To start with, though they won't publicly say it, it seems concussion worries were the main reason for the Avs not to retain Mueller. However, Ottawa has not shown the same hesitancy towards concussed players. Just this week, we've learned they've held negotiations with Jesse Winchester, who had a very similar season to Mueller in terms of concussions, and they also drafted Jarrod Maidens, a player who won't be able to participate in development camp because he still has yet to be cleared from his concussion symptoms. The Senators have already demonstrated a clear willingness to be patient with concussions, and Mueller is symptom-free. He's at greater risk for a reoccurring concussion--that's been medically proven beyond argument--but so is Winchester.
Due to his injury risk, Mueller will be available for extremely cheap. It's highly unlikely he will be able to sign for more than the two million he was making with Colorado, and the production he's demonstrated when healthy makes that a bargain.
More importantly, the majority of the 36 points Mueller recorded in 47 games with Colorado came on the wing, though he is a natural center. He is also a natural two-way player. In short, he is a top-nine winger with top-six upside. Signing Mueller would give head coach Paul MacLean the option of putting together what could only be considered an outstanding third line: Peter Regin, Mika Zibanejad, Peter Mueller. All three players are fast, skilled, and capable of playing in all areas of the ice. All three players are also centers by trade, which means getting kicked out of the faceoff circle is inconsequential to the line.
Adding Mueller also gives the Senators more depth to pursue Rick Nash, or preferably, Bobby Ryan. If Zibanejad is included in a package for a top winner, either Mueller or Regin is perfectly capable of centering the third line, and Colin Greening would naturally bump down to the wing.
Assuming an unlikely trade happens, the team's forwards could conceivably look like this on opening night:
Michalek-Spezza-Nash
Silfverberg-Turris-Alfredsson
Regin-Mueller-Greening
Condra-Z. Smith-Neil
That's a roster that I would put up against just about any opponent in the league and feel good about. It balances speed, scoring, and defense, and lets MacLean roll four lines all season long, and it leaves room for a player like Mueller to slide up if Alfie retires after next season. Regin could take over centering the third line while Stefan Noesen, Mark Stone, or Matt Puempel could safely jump on the line and play sheltered minutes while cutting their teeth at the NHL level. Mueller would also provide insurance should Jakob Silvferberg prove unready to play at the NHL level right away, as he's capable of playing in a top-six role just fine.
Why not sign Mueller?
The concussion risk cannot be ignored, first of all. Just because Ottawa is willing to take risks with other concussed players doesn't mean they'll be willing to take a risk on every concussed player.
More importantly, while I believe adding Mueller gives the team an ideal third line--one that can both provide offense and valuable defensive play--the team already has a glut of forwards to fill out their bottom six players. Even if Nick Foligno and Zibanejad were traded as the rumors suggest, players who'd be battling in camp for some minutes would include:
Bobby Butler
Jim O'Brien
Jesse Winchester (presumably)
Kaspars Daugavins
That's four players fighting just to play a the role of a 13th forward, as regular roster spots will likely be taken by Erik Condra, Zack Smith, and Chris Neil. If a trade doesn't happen--and let's face it, it probably won't--Foligno and Zibanejad get thrown into that mix. And that's before we even consider that it's possible that a guy like Stone could be ready to play in the league before the year is over! That's too many forwards. Adding another to the mix doesn't really make much sense.
Conclusion
Mueller represents a high-risk, high-reward investment for the team. Having watched him in Phoenix (disclaimer: I AM NOT A SCOUT) for a few years, I remain convinced he is a player who would absolutely flourish in MacLean's system. He would give the team depth to create a more effective third line than what was iced last year, add punch and skill to the power play, and the flexibility to play anywhere needed in the top nine. When healthy, he's demonstrated an ability to produce points consistently, and his recent history means he will come at a very reasonable price tag. That's the kind of investment I want to see Murray make, regardless of team need.