why would the canes give up a first on a cap dump

Because that's the cost of doing business if the Canes are going to keep Necas, Jarvis, Suzuki, Drury, and 1 or 2 of their impending UFAs.
Also, if San Jose decided to do a buyout, while the cost would only be a little over $800k per year, the term of the inexpensive 1/3 buyout (Player Under 25) is still rather long.

Because no one wants your cap dump for anything less.

Or, they keep their 1st, and eat the buyout penalty themselves. Like you said, it’s really cheap. 800k penalty, granted over 12 years, isn’t worth moving a 1st for.

I agree. I'm not sure it would even be worth a 2nd to dump him. 12 years is a long time, but the cap hit is negligible. There's also not much risk to a team that would acquire him, because they would still have 2 years to take advantage of the 1/3 buyout, since his birthday is in July and the buyout window is in June. I could see somebody being willing to take a chance on him for future considerations. He looked like he was ready to break out the first part of this past season.

There's one scenario where I think it might be worthwhile for Carolina to give up a pick to dump him: The team they trade him to agrees to buy him out so Carolina can re-sign him for a lesser amount.

Kotkaniemi saga