Who said I wanted infrequent hero death?
If you're trying to run a Pulp-style game, one of the defining characteristics of Pulp stories (as noted in the original post) is the rarity of permanent character death, despite being full of dangerously high-risk actions with crazily high frequency. Your
players are certainly going to want hero death to be as infrequent as possible, in any event, and if high awesomeness only comes with high risk and high stakes, the awesomeness is going to come less often than genre conventions presuppose.
Some tropes are more vital to the definition of their genre than others. Subvert those, you don't have that genre any more; at best you have something that looks like it. If you want to subvert the Pulp trope of infrequent hero death in the name of creating a sense of real risk for the players, you can, and I'm not saying that would make a bad game or a not-fun game. I'm just saying I don't think it will ultimately look or feel much like a classic Pulp serial in practice, because the incentives for the
players aren't going to be the same as the incentives for a classic Pulp protagonist. I honestly think most players interested in a Pulp game for the sake of the Pulpishness itself are far more interested in playing somebody
already like The Shadow than in playing through the half-dozen tries needed for somebody to survive
becoming The Shadow.
(I could always be wrong on that last thought. Anyone with experience to the contrary is welcome to chime in. But my own experience doesn't suggest it.)