It's not clear what you're asking. The justification you list for AIC may well still be a valid one, just not something that applies to all parameteric families. You highlighted a particular family, linear regressors on an m-dimensional variable, where empirical risk minimization might be just fine. That doesn't speak to generic properties about different parameteric families, nor infinite VC dimension families.
From my perspective, I'm not sure I agree that empirical risk plays much of a role in the justification of AIC. As I understand it, AIC represents relative information loss between two competing models, and isn't necessarily intended to be thought of in terms of the optimal choice from a family of parametric models. If you're choosing between a few different models, you might like to minimize the asymptotic KL-Divergence from the "true" model, and it is for this that AIC serves as a proxy.
As an aside, I personally advocate ignoring appeals to unbiasedness in estimators. It's not a genuinely meaningful way to evaluate estimators. Andrew Gelman recently had a short post about this.