Accessibility checker is not very accessible

As someone who often remediates flyers made by other folks, I like Canva: it steers inexperienced designers toward better choices than say, Publisher ever did! As for accessibility though, Canva has been slow to improve. As of this writing, they tend to drop every object into <P> tags, whether they're an image or text, and that kind of feels like cheating, doesn't it?

For most layouts, if you start with the Reading Order panel (in the Accessibility tools, not the nearly-if-not-totally-useless "Reading order" that sits over by the "Tags" tree), you can make sure the text is tagged logically (H1 for the big stuff, <p> for the details, etc.), then artifact all or most of  the stuff behind the text and add or edit alt text where appropriate, then run the checker and there won't be much to fix. Note: it's often easier to double-click on an object to select it rather than trying to drag a box around it, especially in Canva - objects tend to be grouped together or welded to text haphazardly. The point being, the Accessibility Checker isn't adding alt text or tagging willy-nilly, it's just showing you how the doc is tagged and pointing out errors. The wonky tags you describe are more likely a result of Canva's PDF engine, although Acrobat's Autotag can sometimes work in mysterious ways. But when a layout gets complicated and things go off the rails, I've found that AutoTag works pretty well nowadays. Run that, see how it did via the Control Panel, then run the checker and play whack-a-mole with the remaining errors. 

If that still results in garbage, another last resort is to gather all the text (ideally copied from Canva, since sometimes copying from the PDF can scramble text order) and alt text, tag everything as images, and drop all your text in as alt text. A screen reader user gets their substantially equivalent experience, and there's no change to the visuals.

Hope that helps!