I don't know what you mean by "mild steel. Bikes have been built for a century using non-alloy carbon steels like 1020, or comparable. These aren't as strong, so would use thicker walls to compensate, hence making them heavier than a comparably strong high strength steel frame might be.

Also, because the flex property of steel is similar for all grades, the heavier frames tend to be unduly stiff, and ride like trucks.

If you figure the total costs of building, I can't imagine that using a 1020 steel saves enough over a 4130 (the most common tubing alloy) to bother. Yes you can go that route, but why would you?