References regarding optimal and minimum contact area or touch target size on mobile devices (also similar question previously on UXSE here) suggest that the contact area should fit the rough size and contact point on a thumb.
Weighing up the pros and cons for a square or round shaped button or call-to-action, it doesn't seem like there is enough square or round shaped buttons because of the amount of body text and length of characters used on labels and the typical way layouts are structured on webpages that focus a lot more on the width than height.
However, when we look at the proliferation of cards and tiles being used on many mobile apps and website home pages, it seems to suggest that they are more useful in certain types of contexts.
Also, in game interface designs where there is less emphasis on reading text (e.g. in dialogues) and more focus on interactions, buttons don't tend to be rectangular shaped but have shapes that seem to be more fit for the purpose of optimizing the touch area.
With the more common use of voice-as-an-interface and also with more traffic now coming directly from mobile devices, is there any particular reason that there are not more square or round-shaped buttons on user interfaces? Is this a trend that we would expect to see more on the body of a webpage rather than just on the areas of the screen that are more condensed (e.g. menu headers and toolbars)?