Do these bed frames need a box spring?

No. Every frame in this roundup is a platform or storage design rated to take a mattress directly on steel or wood slats with no box spring required. Verified-purchase reviewers consistently confirm memory-foam and innerspring mattresses sit fine on the slats, though a few r/Mattress threads caution that wide-set wire bases (like some Zinus SmartBase configurations) can be too far apart for thinner all-foam mattresses.