At positive rank the whole affine Hecke algebra is not one cyclotomic KLR block

The positive-rank affine algebra is infinite dimensional. At rank one the affine presentation is $F[X_1^{\pm 1}]$ in NG and $F[x_1]$ in DG by [F1], and their distinct powers are independent. More generally for any $d\ge 1$, the NG assignments $T_r\mapsto q_H$, $X_r\mapsto q_H^{r-1}t$ give a surjection onto $F[t,t^{-1}]$: the quadratic relation reads $q_H^2=(q_H-1)q_H+q_H$, the Bernstein relation reads $q_H^2{q}_H^{r-1}t=q_H{q}_H^{r}t$, and the commuting and braid relations are scalar identities. In DG the assignments $s_r\mapsto 1$, $x_r\mapsto t+(r-1)1_F$ similarly give a surjection onto $F[t]$, since the adjacent mixed relation reads $t+(r-1)=(t+r)-1$ and all other relations hold. The images contain $t$, so the affine algebras are infinite-dimensional at every positive rank. Every cyclotomic block is finite-dimensional by [F2], and its KLR partner has the same dimension by [F4]; thus neither is isomorphic to the whole positive-rank affine algebra. At rank zero both presentations give $F$, and the obstruction does not apply.

The whole cyclotomic quotient is not one block. Take $\mathrm{\Lambda }={\mathrm{\Lambda }}_0$ (level one), $d=2$, $e=3$ and $q_H$ a primitive cube root of unity. By the level-one identification [F3] the algebra is $H_{F,q}(S_2)\cong F[T]\mathrm{/}((T-q_H)(T+1))\cong F\times F$, since $q_H\mathrm{\ne }-1$ in characteristic $\mathrm{\ne }3$. Here $X_1=1$ and $X_2=q_H^{-1}{T}_1^2$, so the two factors $T_1=q_H$ and $T_1=-1$ have polynomial eigenwords $(1,q_H)$ and $(1,q_H^2)$, hence residue words $(0,1)$ and $(0,2)$. Thus there are two nonzero blocks $H_{{\alpha }_0+{\alpha }_1}^{\mathrm{\Lambda }}$ and $H_{{\alpha }_0+{\alpha }_2}^{\mathrm{\Lambda }}$, each one dimensional with residue sequences $(0,1)$ and $(0,2)$. Therefore $H_2^{\mathrm{\Lambda }}$ has dimension $2$ and is not isomorphic to either one-dimensional block; on the KLR side [F4] gives $R_2^{\mathrm{\Lambda }}=R_{{\alpha }_0+{\alpha }_1}^{\mathrm{\Lambda }}\oplus R_{{\alpha }_0+{\alpha }_2}^{\mathrm{\Lambda }}$, which is not isomorphic to a single block.

Conclusion. Both branches of the attempted replacement fail: the affine algebra is infinite dimensional, and the whole cyclotomic quotient decomposes into more than one block. Summing the central-sector isomorphisms on both sides remains valid.