What simple arguments and insights can I observe that running both BFS and DFS can be achieved in O(|V| + |E|)?
Intuitively, what a time upper bound of $O(|V| + |E|)$ means is that you spend $O(1)$ time per each vertex and each edge. Taking as an example DFS, there is one recursive call per edge, and the procedure itself runs once per vertex. You can turn this into a full-fledged argument that proves the upper bound.

An upper bound of $O(|V| + |E|)$ is optimal for most graph problems – those that potentially require examining all vertices and all edges. What such an upper bound tells you is that your problem can be solved in the minimal possible time; an $O(|V| + |E|)$ algorithm is an asymptotically optimal algorithm.