Influenza A has two hemagglutinin groups, with stronger cross-immunity to reinfection within than between groups. Here, we explore the implications of this heterogeneity for proposed cross-protective influenza vaccines that may offer broad, but not universal, protection. While the development goal for the breadth of human influenza A vaccine is to provide cross-group protection, vaccines in current development stages may provide better protection against target groups than non-target groups. To evaluate vaccine formulation and strategies, we propose a novel perspective: a vaccine population-level target product profile (PTPP). Under this perspective, we use dynamical models to quantify the epidemiological impacts of future influenza A vaccines as a function of their properties. Our results show that the interplay of natural and vaccine-induced immunity could strongly affect seasonal subtype dynamics. A broadly protective bivalent vaccine could lower the incidence of both groups and achieve elimination with sufficient vaccination coverage. However, a univalent vaccine at low vaccination rates could permit a resurgence of the non-target group when the vaccine provides weaker immunity than natural infection. Moreover, as a proxy for pandemic simulation, we analyze the invasion of a variant that evades natural immunity. We find that a future vaccine providing sufficiently broad and long-lived cross-group protection at a sufficiently high vaccination rate, could prevent pandemic emergence and lower the pandemic burden. This study highlights that as well as effectiveness, breadth and duration should be considered in epidemiologically informed TPPs for future human influenza A vaccines.