First of all, for a particular template to be used for a specific taxonomy term, the template filename should be structured like "taxonomy-{$taxonomy_slug}-{$term_slug}.php". Templates used are determined through a different process than rewrite rules. Rewrite rules determine the query vars used, which only indirectly relate to templates used.
While it’s possible to not have a base permalink term like the taxonomy name in your permlinks, it can cause other problems. When you do that, every permalink generated needs to include a term for that taxonomy. Without a fixed base term, WP cannot tell the difference between taxonomy terms and other slugs that also occur in the first permalink position. Let’s say you have a page titled Renault and a child of that page titled Espace. The permalink for such a page would be example.com/renault/espace/. Without a base term for your taxonomy, the rewrite rule you end up with will take that request and query for a post called Espace which is assigned the taxonomy term Renault. That might return a valid post, but it’s not the page that it was supposed to get. More than likely, the query will come back with no posts found even though there is a valid page with that permalink.
But if your site would not involve such ambiguity, use add_rewrite_rule(). The rule would assign anything in the first position as a taxonomy term and anything in the second position as the brand query var. Your regexp would be similar to the last example with the base term “nutrition/” removed. And of course assigning to taxonomy and brand query vars instead of page_id and food.
Assuming there is a template for the taxonomy term, it’ll be used regardless of the brand specified. If there is no matching term template, unless you have a generic taxonomy template, archive.php is probably the template that will be used. It depends on the templates available in your theme.
