If a team extends the player after the trade, any additional value the player gains by having more team control is cancelled out by the fact that you are extending them at current market value. His value comes from the fact that he is expected to outperform his $8M contract. If they tack on another 5-7 yrs at $125-175M (or 2-3 years for $50-75M, whatever it ends up being), they could just go get a FA for the same price without giving up any prospects.
Long story short, it absolutely matters that he only has 1 year remaining on his team friendly contract.