I want to understand how wordpress is structured in the first place with regard to search engine friendliness. Isn't it set up for SEO by default? Is the SEO plugin necessary then? and to what extent does post name in the url make a difference as against the standard numerical format of wordpress urls?
The main purpose of SEO plugin is to give you more control over SEO-related factors (titles, excerpts, meta tags and so on). It doesn't do anything magical, just an editor to let you fine-tune beyond native WP capabilities.
So necessity equals if and how much of those aspects you are willing to spend time on.
and to what extent does post name in the url make a difference as against the standard numerical format of wordpress urls?
This is considerable factor. URL is important place for determining what page is about by search engines.
I would personally say that it is if you're not willing to build it into your site by hard-coding it in. Wordpress has several limitations when it comes to SEO. For example, the post slugs (used in the URLs) include extra words like and, the, a, etc. This makes the URLs very long an non-search engine friendly. Having the post title in the page title gives you more terms for the search engine to base its search off of. The post names in the URL provides the same effect and are much more user friendly as well.