And 1st. Lieutenants HAVE frequently served as Company commanders in the US Army, depending on the personnel requirements – and frequently, on budget.
But the US military’s tradition is of a smallish professional Army where the formality of rank and posting, based on your CV (Academy grad? combat vet? decorated?), your formal seniority (date of entry? date of commission?), and compliance with the full formal requirements of the promotion (e.g. education, time-in-prior-grade, passing the evaluation with X score) is strictly observed when they can afford to. This military, in time of war has expanded through call-ups of state-militia and “volunteer regiments” (today, the National Guard and Reserve), draftees, etc. and has used brevets, acting appointments, “operational rank”, “frocking”, etc. to cover for losses and/or temporary shortfalls with the understanding it is temporary. (The reserves and National Guard, in turn, mostly promote based on whether there’s a vacancy at the next level and the budget to cover it, so you’re likely to get a bit of “rank deflation” on those troops.)
“Acting” appointments are exactly that: You are still the lower rank, you just ACT as a substitute for a missing higher-up, you’re not even wearing his rank temporarily (“operational rank”). You MAY end up promoted to it either provisionally or permanently, or just fill the post until they get a regular one to fill the post.