Who cares? He should only be using the other 7/8s when nobody else is; that's the entire point. If their virtualization isn't setup to keep people from bogarting resources on a "first come, first keep" basis, that is their poor decision to live with; they shouldn't be taking it out on customers by killing processes and so on.
A VPS host shouldn't be asking or telling customers to manage their own CPU resources, period; that's the point of a VPS in the first place. It's a virtual private server. It should be isolated in a fashion such that even if I'm using 100% CPU 24/7, it doesn't affect anybody else. If a host told me to "use less CPU" I'd tell them to "acquire better virtualization" and find a better host. Ridiculous.
I agree but you should not be using a VPS if you are a high CPU user. You use a dedicated server for that.
Most shared providers will charge you more if you use more CPU or require that you upgrade to a dedicated server. I'm pretty sure that any hosting company will be happy to lose you as a customer if your usage degrades the other users performance.
Being able to use up to your share of a VPS is why you pay for a VPS and not shared hosting. If you pay for 1/8th of a server you are entitled to use 100% of that quota 24/7/365. Using your resources doesn't "degrade" other customers' performance unless the server is set up incorrectly. As long as they can access their 1/8th everyone should be happy.
He can use more than his 1/8 share of CPU time but others can't use his 1/8 share.