To be fair, there are a million ways to look at who and what constitutes as "a team player focused on the greater good". Is a player who signs an outrageous contract at top dollar and therein crippling the team under the terms of salary cap one (ala Doughty)? Is a player who signs above market value with their home team for the final years of their career (ala Kopitar)? I'd say Kopitar fits into the category of such a player when we look at the full picture, despite failing to take a home team discount anytime throughout his tenure with the Kings.
Heck we haven't had a player who signed at a home team discount since Dustin Brown, though Mikey Anderson did take a home team discount on his previous short term contract.
I agree with you in that the last time we had a core of players truly focused on the greater good was back in ~2012 - 2014. Lombardi was great at bringing in character guys and not overpaying come contract time. He had a vision that he consistently shared with the players and got their buy in upfront, and continually monitored for it going forward. Blake appears to be focused more on talent which is great, but it has tipped the scale when it comes to players with leadership/team focus and selfish players (which some of our vet leaders may fall into). But, it is a different era.
In the era of no trade contracts, and the majority players acting as mercenaries seeking the money first and foremost I don't really think any team has a majority of players who care about the team above themselves. Likely the best we can ask for is for players to give it their all, continue to work to improve and hold themselves accountable to perform up to the level of their contract (and hopefully beyond).
As to +/-, I love that stat but we all know it is extremely flawed as a standalone indicator. Gavrikov, for instance, is a -2 on the year, which, by your logic, would indicate he is a low quality defensemen (as +/- is even more important for defensemen than it is for forwards). Given that analytics have evolved so greatly in the past several years, it would be foolish to place too much importance on one stat alone. For instance, how often does the payer start a shift in the defensive zone, what is the quality of their teammates, how sucessful is their team (hard to have a great +/- on a team that is consistently getting wiped by their opponents / bottom of the league in wins despite a single individuals effort), are they contributing in another way such as being a PP specialist ala Ryan Smyth...
With all the analytics out there, though, we still can't confidently say who is a true team first player, and who is selfish.
All we can do is make flawed educated guesses.