I have bills to pay. I'm not what you would call a person of independent means.
Anyhow:
1) In between not knowing the math, and knowing the math, there is learning the math. Very little existing knowledge is presupposed in B&E. There are always some prerequisites, but they're really not that heavy (I didn't study mathematics formally past GCSE, but I didn't find myself completely unable to proceed). Intellectual curiosity is a strong motivating factor for some people - e.g., in theory, those who read philosophy books and talk about them. Writing philosophy books for people who have no intellectual curiosity strikes me as a fairly unrewarding exercise.
2) Nowhere is it claimed that mathematics provides access to being. The claim (or "wager", since it's not exactly a truth-claim as such) is that mathematics "is ontology"; that is, that it lays out just the kind of empty framework, systematically voided of substance, that one might use if one wanted to talk about being without presuming to be able to make any "inroads" into it whatsoever.
3) Neither is it claimed that theorems are politically decisive, or that one should care about them the way one cares about food, shelter, paying the bills and so on. There are however other things it's possible to care about than bare animal survival, and other ways of caring about them. And the different objects and modalities of concern do sometimes link up, in sometimes unpredictable ways, over the course of an average human lifetime. It's why people get baptized, say, or learn to speak another tribe's language so that they can marry someone from that tribe (I was speaking to someone the other day who did this). I get the impression that Badiou's political radicalisation was a life-event of a rather similar sort.
4) The mathematics doesn't have the function of supporting other truth claims by somehow magically "proving" them. It provides a framework for making the various things you're claiming consistent with each other. They might all be false at once; the point is for them to be consistently false. (Also, of course, the consistency of Badiou's "meta-ontology" is not as rigorous as the consistency of the mathematical "ontology" it tracks - the one isn't a model for the other, although the mathematical concept of model does provide a metaphor - and it is no more than a metaphor - for their relationship).
5) If there can be left-Heideggerians, there can be left-Platonists.