It remains unclear why acute depletion of CTCF (CCCTC-binding factor) and cohesin only marginally affects expression of most genes despite substantially perturbing three-dimensional (3D) genome folding at the level of domains and structural loops. To address this conundrum, we used high-resolution Micro-C and nascent transcript profiling in mouse embryonic stem cells. We find that enhancer–promoter (E–P) interactions are largely insensitive to acute (3-h) depletion of CTCF, cohesin or WAPL. YY1 has been proposed as a structural regulator of E–P loops, but acute YY1 depletion also had minimal effects on E–P loops, transcription and 3D genome folding. Strikingly, live-cell, single-molecule imaging revealed that cohesin depletion reduced transcription factor (TF) binding to chromatin. Thus, although CTCF, cohesin, WAPL or YY1 is not required for the short-term maintenance of most E–P interactions and gene expression, our results suggest that cohesin may facilitate TFs to search for and bind their targets more efficiently.