If you steal a Mercedes someone else goes from having a Mercedes to not having a Mercedes so is materially worse off. If you stream live sports from someone other than the rights holder then the rights holder is no worse off than if you hadn't watched it at all.
If you want to buy a car but think a Mercedes is to expensive then you can get a cheaper brand. I have a 2007 Honda which thinks it's a Mercedes - leather seats, all electrics, 5 star safety rating. If you want to pay for streaming football but think Sky is too expensive then there is no paid alternative. And the exclusive rights model prevents competitors entering the market and driving prices down.
Also those American sports with great streaming or on demand services you mentioned - I'm pretty sure Sky has the rights to those in NZ too so from their perspective watching NFL on a paid stream though a VPN is just as much a violation of their rights as watching it on an illegal stream.
Consumers in NZ demand a paid streaming service. Sky realised that it could charge more because there was no competitor to undercut it, so it did. As a consumer you can either take Sky's shark and keep paying more and more for an inferior product or walk away. Once you've walked away it doesn't make any difference to Sky's bottom line if you illegally stream or not.