> a fun way to consider an upper bound on the total number of board states and therefore how hard it is to 'solve' chess compared to a game like checkers

That and therefore doesn’t follow. As a counterexample, consider a NIM (https://en.wikipedia.org/wiki/Nim) game starting with a googolplex number of piles of size 1. That has way more board states than chess or go, but is easily solved, as the game is trivial.