It's difficult to envisage charging for the distribution ending well, but you can already pay Canonical for support if you'd like to, and I'm sure they'd be happy to tell you how to disable the "advertising". TBH, though, I'm not sure how Canonical's relationship with Amazon search is any different from what Mozilla do with Google search.
Actually reading more about it: this is using Amazon's store search, not their web search as I initially thought. It's also getting money by adding referral codes, rather than Amazon paying Canonical to have their search engine listed. So there's some differences after all.
It's difficult to envisage charging for the distribution ending well, but you can already pay Canonical for support if you'd like to, and I'm sure they'd be happy to tell you how to disable the "advertising". TBH, though, I'm not sure how Canonical's relationship with Amazon search is any different from what Mozilla do with Google search.