If you’re concerned about the performance I would recommend using the WordPress API instead of trying to load markup using ajax.
If you look at wp-includes/template-loader.php you can see how WordPress itself figures out which template to use. You could in theory just load that file, but you might have problems with template_redirect.
require_once( ABSPATH . WPINC . '/template-loader.php' );
Alternatively, you can just copy paste the code you need.
$template = false;
if ( is_embed() && $template = get_embed_template() ) :
elseif ( is_404() && $template = get_404_template() ) :
elseif ( is_search() && $template = get_search_template() ) :
elseif ( is_front_page() && $template = get_front_page_template() ) :
elseif ( is_home() && $template = get_home_template() ) :
elseif ( is_post_type_archive() && $template = get_post_type_archive_template() ) :
elseif ( is_tax() && $template = get_taxonomy_template() ) :
elseif ( is_attachment() && $template = get_attachment_template() ) :
remove_filter('the_content', 'prepend_attachment');
elseif ( is_single() && $template = get_single_template() ) :
elseif ( is_page() && $template = get_page_template() ) :
elseif ( is_singular() && $template = get_singular_template() ) :
elseif ( is_category() && $template = get_category_template() ) :
elseif ( is_tag() && $template = get_tag_template() ) :
elseif ( is_author() && $template = get_author_template() ) :
elseif ( is_date() && $template = get_date_template() ) :
elseif ( is_archive() && $template = get_archive_template() ) :
else :
$template = get_index_template();
endif;
/**
* Filters the path of the current template before including it.
*
* @since 3.0.0
*
* @param string $template The path of the template to include.
*/
if ( $template = apply_filters( 'template_include', $template ) ) {
include( $template );
}