1 People can easily leave your site
When accessing an AMP page, users remain inside Google's ecosystem. A user can very easily leave the site by clicking on the cancel button on the top of your amp page. This makes the process of leaving your page almost effortless.
2 Ads bring less money
According to reports, ad revenues with amp are around 50 to 75% of revenues without Amp due to Amp's limitations. See why Ads are bad for your site.
4 Very hard to implement for dynamic pages
Amp is very hard to implement for dynamic pages and is more suitable for static pages that don't change such as news sites.
5 Difficult to administer
Amp requires webmasters to maintain two copies of their site and to make sure that content is published on the two sites. There are some workarounds for this step using some web plugins but there is still more administrative headache with Amp.
6 Bad for branding
Amp strips a site of some of its basic elements and makes it a part of Google's ecosystem. This reduces the brand image. See the importance of branding.
7 Hard to implement on E-commerce sites
E-commerce sites might have problems implementing Amp pages, as the reduced functionality might prevent them from including all the needed options.
8 Limited design options
With Amp, a person must choose from between very limited styling and design options. This could hurt brand image.
9 Risk of duplicate content
If proper tags aren't added, the risk of duplicate content might be there and the site might get a penalty by Google. See also how Google panda work.
10 Optimized sites can be as fast as amp
According to some bloggers, a very well optimized site can actually load as fast as amp; thus reducing all the headache needed and achieving the same results.