Q.What about the kinetic friction between the road and the tyres (on a banked road)?

The speed-limit analysis uses STATIC friction because the tyres roll without sliding. …

On a banked road, as long as the vehicle's tyres roll without slipping, the contact patches are momentarily at rest on the road and the friction available is STATIC — this is what Eqs. (1.3)–(1.4)'s limits are built from ($f_s \leq \mu_sN$). If the vehicle goes slower than $v_{min}$, it begins to slide DOWN the incline; faster than $v_{max}$, it slides UP and outward. From that instant the relevant friction is KINETIC: direction opposite to the slide, magnitude $\mu_kN$ with $\mu_k < \mu_s$. Because the kinetic value is smaller than the static limit whose exceedance started the slide, the net unbal …

Compare regimes with numbers: for μs = 0.5, μk ≈ 0.35, recompute Eq. (1.3)'s v_min using μk — the sliding vehicle would need an even wider window than the one it already …

Using μk in the speed-limit formulas (they describe rolling, i.e. static-friction, conditions); assuming friction 'switches off' during a slide …