Tsunamis cause significant damage and loss of life, particularly for the nearest communities, where the tsunami may arrive in minutes. These local communities often do not receive an informed or timely alert under traditional warning pathways. In response, numerous tsunami early warning (TEW) algorithms have been developed with the goal of providing informed tsunami source characterization for use in rapid, localized warning. An overlooked aspect of TEW is the means that this crucial information is disseminated. Current operations focus heavily on the time an alert is issued from a warning center, however, that alert passes through multiple groups and agencies before it is conveyed to affected communities. This distribution path can create further delays and contributes to inconsistencies in the message timeliness and content. In this study, we provide the framework and advocate for the use of a rapid dissemination tool, that we call WaveAlert, that would leverage preexisting advances in earthquake early warning systems to provide timely, clear, and consistent alerts to the public by use of the MyShake EEW phone app. This proposed tsunami dissemination tool would be able to provide consistent, public facing tsunami alerts over the duration of the hazard with the added benefit of low message latencies and high spatial resolution in who can be targeted for messages. We illustrate the need for rapid alerting strategies through a retrospective look at the alerting process during the 2022 Tonga tsunami and through a modeled potential near-field Cascadia timeline example affecting the west coast of the US.