A young star can have leverage. It depends on the situation. Look what Nylander, Marner, and Matthew's were able to get.
If Suzuki puts up big numbers next year, he could say: pay me my worth or trade me to someone who will. It depends on how well he does, and how he wants to handle the negotiations.
I think we're looking at his all wrong. It's a stance of conflict, not negotiations.
Why people should worry about Suzuki's contract (more so than KK's, who will undoubtedly be bridged) is that, if Suzuki shows consistent progression throughout this year and next, we should, perhaps, look to benefit from a smaller long term Cap hit by signing him long term and factoring in RFA years remaining to bring down the AAV (provided he's willing to sign long term for the security, unlike the recent 5-years trend for young star players)
In the short to medium term, it means making sure there is Cap space to extend Suzuki, keep aligning quality depth and have enough left over to extend\bridge other youngsters.
You set your prospect hierarchy and, if Suzuki is to be your #1C, it is reasonable that you priorritize his case and bridge other prospects.
In the late medium to long term, you will benefit from added flexibility to keep icing a contender for more years because of his lower AAV.
We saw it with Subban -- bridging Star players will come to bite you in the arse down the line, with huge AAVs to cripple your Cap.
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