I will discuss cosmic strings associated with axions arising from extra-dimensional gauge fields, with a focus on their impact on axion dark matter. Unlike more common 4D setups, resolving the string cores, which is necessary to make sense of the strings' properties and cosmology, demands a higher-dimensional UV-complete description. In arXiv:2312.08425 [hep-ph], we took it to be the closed string axiverse, for which I will argue that the presence of cosmic strings can lead to overproduction of axion dark matter regardless of the axion mass. I will then present how the multiple axions of the axiverse may alleviate that conclusion.