To be a bit more specific as to how _decoherence_ solves this, one way to see it is that classicality (i.e. observables having specific values) is an emergent property in the limit of near-infinite degrees of freedom in the same way that e.g. thermodynamic properties (temperature etc.) are emergent properties of classical systems in the limit of near-infinite degrees of freedom.
Putting it on the edge, claiming that quantum theory is at a dead end is like claiming statistical physics is at a dead end.
One of my personal favorites for how to formalize this is the work on "pointer states" by Wojciech H. Zurek. There is a freely available Physics Today articls [0], and you can find surveys of further work e.g. in the introduction of [1].
[0]: https://arxiv.org/abs/quant-ph/0306072 Zurek, Decoherence and the transition from quantum to classical -- REVISITED [1]: https://arxiv.org/abs/1508.04101 Brasil, Understanding the Pointer States