Okay let's spell it out
Do any of Chicago/Anaheim/Pittsburgh/Tampa Bay (class of the league imo) have 2.5M allocated to a guy who can literally do one thing (on the 4th line)? No
We play a puck possession game - Does Martin have any puck skills? No
Is he going to be tradeable later? Maybe. No one else wanted him at 2.5M for 4 years apparently because we managed to sign him.
Can you sign someone else who literally does this one thing (hitting) for less? Probably. Ryan White is available. Rinaldo was available for on waivers.
"But character, intangibles, and toughness" - These are ways you describe people who are bad at hockey - Clarkson, Bolland, Armstrong - This is the exact same type of addition, just a different name.
The main point is the original one- It's a stupid signing that has a lot of outdated thinking behind it. None of the best teams employ this type of player. It's about a speed, skilled and possession game.
Fighting doesn't matter in the playoffs, you might get one fight in the entire post-season. If you think you need need this type of guy to win in the playoffs, the Islanders have only won 1 entire post-season series (just recently) when John Tavares went legendary against Florida. This was despite having the *best* 4th line in the entire league.
If you think toughness is a detriment, tell that to Marc Savard - team of Lucic, Chara and Thornton and the dude got knocked out....
There. I spelled it out.