They are not 'relying' on the Sedins. Check the time on the ice. The twins are getting 3rd line minutes ~14 mins per page. The problem is there is no depth overall. It is what it is, the window closed quickly on the team and they were slow to retool on the go. So here we are.
The Sedin's signed a contract at a discount, with the organization knowing they would be paid 'too high' in the last couple years of the deal but were able to have more cap space in the near term when they made a couple runs.
That being said, I was excited after game one, with the style and pace of the play. It has steadily dropped off since then. Getting hard to watch, like last year.