He has full NTC so any trade discussion has to begin with an assumption that he is asking for a trade which typically hurts trade value. Fans are typically disappointed in the returns of star players. It is tough to win a deal where you move the best player, especially in the short term. All of that said, you present a legitimate perspective.
On the other hand, my question is: has an asset like Larkin been traded recently?
Quality 1st line player, prime aged, long term value contract. There is absolutely no uncertainty attached to Larkin which is the exact opposite situation of any star player trade I can think of.
Star's that are traded are typically pending free agents, have injury concerns, are overpaid, or demand out.
In Larkin's situation any version of this would probably fly under the radar for a while. Why? Two reasons. 1) I'd guess Larkin's top priority in this hypothetical would be playoffs/competing implying some level of flexibility on his landing spot 2) I don't think he'd want to completely sewer the organization on the way out so the "demand" would be more so of the nature of "let's work together to find a win-win change for Larkin and the Red Wings"
Yzerman runs a tight ship and because of the contract has no obligation to trade Larkin. I think trade talks would fly under the radar mitigating the impact the NTC has on the trade value.
All of that said, I'm probably talking my self into hypothetical disappoint because of my first paragraph. It just seems like a unique scenario. Realistically the range of outcomes is somewhere between Horvat and Rantanen imo.
Regardless, other than off season BS'n were a long ways away from this hypothetical.