Using taxonomies to handle layout?

Taxonomies are sort of overkill in this case. Taxonomies are not required to have an archive page (they can be used for internal things only). Your nav menus, for example, are terms in a taxonomy — just a way of grouping content that belongs together. What you’re talking about is a bit outside of that scope.

I’d suggest you create a little meta box. Give yourself whatever options you need, and filter post_class to change the styling. You can also, of course, include or not include things based on a postmeta value. Here’s an example.

Then you just style with css, using selectors like .post.left_thumb or something similar.

Or you could grab the meta value in your single.php and change the layout based on that.

<?php
$layout = get_post_meta( $post->ID, '_wpse32973_layout', true );

if( 'left_thumb' == $layout )
{
    // do stuff
}
else
{
    // do other stuff
}

You could also use template parts and avoid some if statements in your templates.

<?php
$layout = get_post_meta( $post->ID, '_wpse32973_layout', true );

// make sure layout always has a value.
$layout = $layout ? $layout : 'some_default_thing';

get_template_part( 'content', $layout );

Anyway, lots of options to avoid a taxonomy, which I think is not a great choice for this situation.