In that case Google should be free to not index his page, or at least not show it to users who Google know are not interested in downloading it.
No, it shouldn't. Google should reflect an accurate ranking of pages based on content relevance (as best as possible technically), not a curated list.
Too much to be left to some private interests to play with at their own opaque will (and sell to the highest bidder).
The evidence that visitors find bloated pages an issue is slowly growing, from Amazon quantising the financial loss of slower loading pages [1], to more recently, Life Hacks taking advantage of GDPR-triggered quicker-loading less-bloated European-versions of news sites [2].
I guess the question worth asking is if a non-AMP page is objectively more-performant than an AMP version, does Google prefer the publisher to keep the slower AMP version?
In a sense AMP is user-focused, validating Jakob Nielsen's prediction of the end of Web Design, because "people spend more time on other sites" [3].
[1] https://www.fastcompany.com/1825005/how-one-second-could-cos... [2] https://lifehacker.com/to-make-websites-load-faster-browse-t... [3] https://www.nngroup.com/articles/end-of-web-design/