An impressive effort by the scientific community has quickly made available SARS-CoV-2 vaccines, indispensable allies in the fight against COVID-19. Nevertheless, in liberal democracies, getting vaccinated is an individual choice and a not-negligible number of persons might turn out to be vaccine refusers. Behavioral and Cognitive (B&C) scientists have cast light on the key behavior drivers of the vaccine choice and suggested choice architectures to boost vaccine uptake. In this paper, we identify a somehow neglected psychological phenomenon, that it is reasonable to believe to hamper the vaccine uptake whereby fine-based coercive policies are in place. We begin by presenting the default effect, peer pressure, and the case versus base-rate effect as examples of psychological mechanisms relevant for vaccine choice. We show interventions on the choice environment conceived to manipulate such mechanisms (§1). Next, we focus on what B&C scientists have investigated as well the conditions under which monetary disincentives become ineffective policy measures. To do this, we discuss in detail the case of the crowding-out effect (§2). In section 3 we present the original point of the paper. We argue that imposing monetary disincentives on vaccine hesitant could turn out to be ineffective also because of the human tendency to keep options open, albeit doing so bears some cost. In section 4 we draw an experiment aimed to begin testing whether the tendency to keep options open factually plays a role within the context of the vaccine choice (§4). Finally, concerning the COVID-19 emergency, we defend an attitude of epistemic humility in translating behavioral and cognitive research results into policy suggestions (§5).