He's an RFA. If Carolina wants to sign him for cheaper than his contract demands, their only option is through an arbitration hearing. Necas's camp will, like you said, point out that he had 70 pts last year and 60ish this year, and was a great playoff performer this year and decent last year.
Necas will point to guys like Meier, Debrincat, and Terry who all filed for arbitration and had similar stats to him at time of signing. Those contracts run between 5-8m in terms of salary which is what Arbitration cares about (although Suzuki, another similar player, just got 10m). Carolina has 27m with Jarvis, TT, Guentzel, Drury, Pesce and Skjei needing contracts.
Jarvis will rightfully want more than Necas. If Carolina wants to stay competitive (seems likely) they need to at least keep Pesce and Drury too. Or at least according to their fans they want to keep Pesce really badly. Drury probably won't get much but he's been good in the playoffs. Could see that going to Arbitration too.
They need at least 5 players signed with that 27m. Jarvis I can't see taking any less than 7 and will probably get more than that, but lets assume 7. That's 20m for 4 players now.
And these guys aren't the 3rd and 4th liners for Carolina. These are 4 players in the top 6 who need to be signed or replaced. Even if Drury only gets like 2m, there is just no way Necas will be happy getting 5 or 6. I believe it was reported he wants 8 something. Carolina just can't afford that.
So they have two options. They can either go to arbitration, which will probably be 1-2 years given that Necas has already said he wants to play center and doesn't intend on signing long term with Carolina, and hope that Arbitration awards him a 5m contract and they can give him a bunch of performance bonuses to keep him happy that won't impact the cap...or they can trade him.