The clique-count conjecture for complete minor-free graphs

Let $\textup{cliques}(n,t)$ denote the maximum number of cliques in an $n$-vertex graph with no $K_t$-minor. Clique-count conjecture.

$$\textup{cliques}(n,t)=2^{t-2}(n-t+3)\quad\text{if and only if}\quad t\leq 49.$$

The bound is motivated by complete multipartite graphs, and computer search verifies it for $t\leq 49$; examples based on $K_{c\times 2}$ disprove the bound for sufficiently large $t$, including every $t\geq 62$.