In the context of a web application where we handle only one command per request in a stateless fashion, could somebody point me to concrete examples of things that could go wrong if we do not load/save aggregates as one atomic unit? Why do we insist on not to partially load/save aggregates? What are the fundamental reasons behind this rule of thumb?

I could only think of caching but I think there is more. Maybe inconsistency by concurrent writers?

Notes: I have read Eric's blue book up to the end of Aggregates chapter, iterated over most of the questions in SE and SO about aggregate persistence, and watched a few DDD courses on Pluralsight, but I could find a direct and detailed answer.

Thank you