You are entering a very long and deep rabbit hole with a 2000 year history. Your questions are the central issue in epistemology, a branch of philosophy. The philosophers have endlessly discussed the validity of reason and logic which ultimately reduces to defining a valid theory of concepts (or abstractions). The best overview of this history is the introduction to Rand's book "For The New Intellectual".

>By abstracting a system we can work with the essential relationships and features without getting caught up in details and exceeding our working memory capacity.

You are on the right track here. In Rand's "Introduction To Objectivist Epistemology" (where she spells out her theory of concepts) she identifies this as a fundamental cognitive need. As she put it, concepts are "space" savers that allow us to condense the world of experience into a manageable set of abstractions/concepts. The fundamental epistemological question is how do we define/use concepts without falling into contradiction or thinking in a circle.

BTW, Rand is not popular on HN so you won't get much discission here but read and judge her work for youself.