Now, let's model a voter as selfish. German voter (in the pre-war sense) can expect greater benefit with a leader that speaks of benefits to specifically German people, than with a leader that speaks of a benefit to the people in general. This gave an edge to NDSAP.

I don't think voters, even in Weimar Germany, are very well modeled as selfish agents. The NSDAP certainly benefited from proclaiming -- often and loudly, as you say -- their allegiance to the German volk, but I model that more as a way of positioning themselves as the party of German pride: a pretty clear political niche, at the time, and one that could easily be framed as promising restitution for perceived or actual wrongs rather than exploitation of others. (Though you don't need to be a Nazi to be excellent at rationalizing the latter as the former.)

After six years or so of Nazi rule, they did manage to finagle this into a justification for genocidal expansionism, but that isn't the choice that was presented to German voters in 1933.