Yes if you try to carbon copy other teams, you become a poor version of them. There are elements you can take though.
We had no physical presence, Foligno/Simmonds didn't deliver but MTL finished all their checks. We need to figure out how to make the team better for when things change from reg season vs post-season.
I don't want to copy the Isles specifically, just saying spreading the $$ around can help.
I would not spread the money around on depth guys. You can trade Marner, but that money is going towards another high end core player (almost certainly a forward) and any left over money (not that there should be much) can be distributed elsewhere.
I also think focusing on physicality has only created problems for us. Foligno was a non-factor brought in for grit. Clifford was the year before. Simmonds and Thornton had their moments but ultimately were non-factors for the most part. Bogosian and Muzzin were really the only ones that have panned out over the years and that is also because they are good in a lot more important areas (defending). Our top performers this year were all skill guys who were willing to step up (Kerfoot, Nylander, etc.). Not necessarily with physicality and hitting people or even sacrificing the body more than absolutely necessary, but they would drive the net, work hard, and making smart plays consistently.
We need skill, but we need skill that can do more than one thing. Matthews can do more than one thing, and I have complete faith in him being a major playoff performer. He plays the game the right way. Marner, however, is simply an elite playmaker and just being able to pass is not going to help us win.
I am also more concerned about forechecking ability and ability to play in tight, which I don't consider "physicality" because you need skill and IQ to do that as well. I have seen "physical" players who are brutal forecheckers (usually because they don't have the speed, but also because they don't have the IQ and skill) and may be handfuls in tight but they don't have the hands to finish off or make plays even if they win physical contests. I would not want those guys any more than a guy who is all flash and no substance.
Laziness and complacency is not tolerated under any circumstance, but seeing a guy running through the boards does not guarantee he is not lazy or complacent (especially if it leads to stupid penalties, like Kadri's) and conversely, not doing it does not mean a guy is not working hard and doing the right things (which is why Nylander is actually one of the better guys at winning board battles and scoring net front goals).