Vertical ground accelerations do not induce critical conditions to structures - for example given the large capacity of columns to withstand compression load. Columns are relatively slender members in the direction of horizontal motion, hence that ground displacement/velocity/acceleration component generally used for design.
EC8 does give equations for the vertical effect of seismic motions. However, in the profession there is a feeling that vertical loads do not need to be evaluated and so they are disregarded by some software. Recent large earthquakes and in events with pronounced near field effects, vertical accelerations are very important and should be evaluated separately.