For Schema.org metadata, the featured image of a post is used as the image property. For this property, Google Search requires:

The URL to an image that is representative of the article or AMP story.

Due to format differences in search results, the following image guidelines only apply to general AMP pages, not AMP stories. AMP stories have different requirements for images.

• Only a marked-up image that directly belongs to the article should be specified.
  Images should be at least 1200 pixels wide.
• Every page must contain at least one image (whether or not you include markup). Google will pick the best image to display in Search results based on the aspect ratio and resolution.
• Image URLs must be crawlable and indexable.
• Images must represent the marked up content.
• Images must be in .jpg, .png, or .gif format.
• For best results, provide multiple high-resolution images (minimum of 800,000 pixels when multiplying width and height) with the following aspect ratios: 16x9, 4x3, and 1x1.

There is currently no guidance offered by the plugin for the featured image that is selected for a post. There should be a warning when the image is not 1200 pixels wide.

If the requirements are not met, should the image be excluded altogether? Is it better to have something rather than nothing?

We need to avoid situations where Google Search Console informs users of problems related to pages that the AMP plugin generates.

See also plugin forum topic.