We study mixing and diffusion properties of passive scalars driven by generic rough shear flows. Genericity is here understood in the sense of prevalence, and (ir)regularity is measured in the Besov-Nikolskii scale B\alpha 1,\infty, \alpha \in (0,1). We provide upper and lower bounds, showing that, in general, inviscid mixing in H1/2 holds sharply with rate r(t) \sim t1/(2\alpha ), while enhanced dissipation holds with rate r(\nu) \sim \nu\alpha /(\alpha +2). Our results in the inviscid mixing case rely on the concept of \rho-irregularity, first introduced by Catellier and Gubinelli [Stochastic Process. Appl., 126 (2016), pp. 2323-2366], and provide some new insights compared to the behavior predicted by Colombo, Zelati, and Widmayer [Ars Inveniendi Anal. (2021)].