The parameter regime of interest is monumentally out of reach to experiments. We can already derive things on paper about that regime, and with better computers

The parameter regime of interest is monumentally out of reach to experiments. We can already derive things on paper about that regime, and with better computers we would indeed be able to make more complicated calculations about that regime. But to get something useful we also need to "fit" these calculations to observations. We do not have observations not because of a fundamental constraint, rather because it is engineeringly impossible to reach these energy scales with anything we can imagine. So the roadblock is experimental and a quantum computer would not be particularly helpful with it.