Each member’s “page” is actually a “post” as they are all saved as a custom post type. The member post will use the same template that your current theme uses for standard posts. There is no option, even with regular post types, to select a template in the post editor. You are stuck with whatever your theme has set for the post template, UNLESS you create a new template for the custom post type.
I follow the guidelines that plugins should focus on functionality, while themes focus on appearance. If I included a template for the member custom post type, it would either need to be copied to your theme’s template directory, or I would have to intercept the template lookup and force my own template in there. Either way, it would then screw up the appearance of your site since my template would be different than what your theme is using for the rest of the site.
What you need to do to make a full width template for the member post type is to either create a new template for your theme, or copy and rename the template you want to use. Note that a full width PAGE template may or may not work very well as a full width POST template, but that might be the first thing to try… copy the full width page template to a new file in your theme’s template directory and name it:
single-member.php
See these links for more info about templates and template hierarchy:
https://codex.www.ads-software.com/Post_Type_Templates
https://codex.www.ads-software.com/Template_Hierarchy