Because he wants to be in Nashville. So he'll compromise on term, not push for big money, and he saw the way the franchise handled Rinne at the end of his career, he'll understand that they'll take care of him. It's a bit different than in some other places. But I do see the team being willing to go to 6 years. It wouldn't shock me if Saros took just 5, but I think they can settle on 6.
If he wanted 7 or 8 years, or if he wanted the NMC clause, then he has every right to ask for those, but then that would be just like asking Trotz to trade him, and Trotz would accommodate him and trade him. Saros doesn't want to be traded somewhere else, he wants to be in Nashville. So they'll be able to compromise.
Nashville is great and I could certainly understand his desire to stay there and give a bit of a hometown discount.
That's a big ask though to leave a lot of money / term on the table though and assume the team will just "take care of him" after his playing career, when likely new management and potentially even new owners will be in charge. Not to mention the league monitors how much former players make in their roles with former teams to ensure it's within the range of normal salary for those types of positions, so there's a limit as to how much he can realistically make up.
A year ago, Sorokin signed an 8 year, $66M contract with significant trade protection (4 year NMC, followed by 4 year 16 team no-trade list). He struggled this season and was benched for all but 1 game in the playoffs - which he got pulled from. Maybe he'll bounce back given his track record, but goalies are ridiculously volatile.
Hellebuyck signed a 7 year, $59M deal last summer and had a great regular season but struggled once again in the playoffs.
Those are the comps Saros is looking at...maybe he gives a bit on AAV and comes down to 6 years - but that puts him at 35 years old for his next contract, so maybe he's looking at one-year deals from then out at a likely lower AAV than he can secure right now.
As much as I'm sure he wants to stay there, I absolutely don't see him taking 3-4 years and 5-6 would surprise me as well. He could give up some on the AAV especially being in a no income tax state, but I think he still goes 7-8 years as a likely top 5 goalie in the league. Have to feel that this all gets sorted out before the draft, right?