Assume a factorial design with three factors with two levels each. At interim analyses it is found that one factor is associated with severe harm (or strong positive effect), and thus it seems redundant to collect more data with respect to this factor (thinking in terms of Bayesian sequential design). What would the implications be if this factor was dropped and the number of allocation conditions reduced?

If we consider that the analysis consists of a normal regression model with each factor represented as a covariate, I see no concern for dropping one factor when I have the data I need to shape the uncertainties in ways that is important to me. It may of course reduce the power available to me for interactions - but it would also mean that I can allocate participants to the other conditions at a quicker pace and close out the trial earlier.