Risk‐targeted spectra for seismic design have been proposed in earthquake engineering literature to harmonize seismic reliability for different structures designed at different sites. Such a proposal has been motivated by the fact that designing for uniform seismic hazard across building sites has been shown to generally lead to non‐uniform seismic risk. This note uses a case study implementation of the risk‐targeted design actions philosophy for seven Italian sites, to showcase two noteworthy practical issues with this otherwise appealing approach. First, at lower‐to‐moderate‐hazard sites, which may be the majority in a country, design against gravity loads and detailing according to minimum code requirements, can result in higher‐than‐anticipated overstrength, not commensurate with the adopted level of seismic design loads, thus deviating from the target reliability. This leaves only higher‐hazard sites with real margins for homogenization of reliability, which raises the bar. Second, risk‐targeted spectrum approaches typically require some a‐priori assumptions for structural fragility at low‐performance objectives, corresponding to alleged high damage. These assumptions, among others, carry an implicit adoption of shaking intensity measures with which to express fragility, whose lack of sufficiency and efficiency may in turn reduce the level of homogenization of risk that can be achieved.