The players have a role in it, but let's not act like the city creates a sane operating area. You can have talented employees, but if the organization is bad, they employees struggle.
Every outlet in Toronto gave these players the trophy before they had even won a series. It was "How many cups will they win?" It was the fans calling Matthews the best player in the world when he isnt. His 4 goal debut was taken as this "Matthews is the greatest pure goalscorer ever". Fans propped these guys up as messiahs saving the city. They perform when the stakes aren't raised. When the organization lets them play freely and things are light, they are really good. However, 2-3 first round losses in a row, and now doubt starts creeping in. Fans started to ask if the team had the mental mindset. The organization starts bringing in vet players to "guide" these young kids that are supposed to be saviors and show them how to win. However, these vets get hurt (Muzzin), aren't proven performers themselves (Tavares), or are too old (Tanev, OEL, Laughton). Now there is even more pressure on the core young guys to perform, and they still struggle.
Now, after years and years, the fans have turned on the core, and when they lose 2 games in a row, every media question to them is "can you break the curse?" "Can you shut out the demons?" etc. and the entire city is feeling this dread of being a perpetual loser.
The players have fault. The media has fault. The fans have fault. It's not 100% one way or the other. You wanna know what would help the core 4 out? Some depth and defense that was actually competent. Domi was the only decent round 2 performer. Knies didnt look good, they benched Nic Robertson, their defense produced nothing on offense... So everything falls onto a core 4 that 1) have never shown they can compete and 2) were propped up by the same fans that are tearing them down.