I really like black jason for the way that it could mean something about a black man existing in a military camp that clearly values him for his status and how useful he is as the perfect roman soldier and leader, rather than actually caring about him as a person (something that jason remarks on in the books himself and expresses discomfort with), and then proceed to tell a story about this black man regaining his autonomy and reshaping his identity with his own hands and being able to make his own choices about his life - which allows a thematic throughline to the real struggles and triumphs of diasporic black people !!!
so the idea of an all-american golden boy, an almost essentially white male figure embodying western partiarchal values, being black instead isn't unheard of in media and in real life (he's literally not american lol but jackson from the tv show "sex education" is both a good example of and subversion of the trope when appearing in a black character); the golden boy is usually an athlete, handsome, conventionally masculine, talented, comes from a "good" family, experiences favoritism, has strong principles, etc - all of which applies to white jason (the "good family" being jupiter, which awards him the highest possible status among the romans - and thus causes jason's supposed favoritism that he detests). but for a black "golden boy", there can and has been an added connotation of racial exploitation by dominant white power structures that have superficially uplifted him (I recall reading some really good papers in college about black football/basketball stars being exploited for their bodies/labor on both the collegiate and professional level, though I can't remember the names of said papers. exploitation of black men in sports is a big and easily researchable topic tho)
I think this connotation of exploitation would matter because although hera seems to be soft for jason in some ways later on in the series, in tlh she uses really specific, unpleasant language about her ownership of him that evokes much more obviously violent imagery if she now becomes a powerful white woman claiming ownership over a black teenager, rather than a white one (I'd like to note that this is also almost exactly what hazel goes through with gaea, which I've posted about before here and here - though to my knowledge gaea lacks a specific race/human skintone whereas we do know that juno appeared explicitly as a white woman to frank's mom when he was a baby). this is even more uncomfortable if this renders beryl grace a black woman who had her son taken away by an omnipotent white power figure (juno/hera). jupiter "gives" him to juno as a "gift" and names jason after juno's favorite mortal, rather than beryl choosing his name - as if to completely strip jason of his black roots and forcibly assimilate him into her own culture (which is just. a thing that did actually happen to enslaved black people, and why most black americans have """white"""-sounding surnames to this day, including myself)
jason rejects these claims of ownership immediately, and a continuous theme of his character is extracting himself from the repressive confines of camp jupiter, a camp that canonically has ties to the american confederacy as well as a history of racist discrimination against frank's ancestor shen lun. camp jupiter highly values collective strength and militarism, and is in general very old conservative-coded (hence why a lot of people read octavian as a somewhat conservative figure). the existence of reyna as one of its leaders unfortunately doesn't negate this conservatism, but it's interesting how, in having his memories wiped, (black) jason can gain the opportunity to view the world through a completely new lens and attempt to rediscover himself, especially while surrounded by other people of color like piper and leo (idk, especially piper? black-indigenous solidarity runs deep in america, and there's a reason why 'bipoc' is its own category)
in this way I like how jason reevaluating his relationship to camp jupiter, how "roman" (= white/conservative) he actually is, and how much he needs to find himself again after everything he's been through could then be read as a black man freeing himself from an exploitative white power structure that doesn't really care about him. it's an imperfect metaphor that gets icky when taking into account how most of hoo's nonwhite cast starts roman and stays roman (reyna, frank, hazel) but I don't think the metaphor necessarily needs to be read in the exact same way for every character (i.e. frank's eventual praetorship over camp jupiter could be interpreted as a triumph over camp jupiter's past sinophobia)
naturally all of this necessitates some "rewriting" of jason, i.e. his awkward commentary about the confederacy to hazel in moa should absolutely become a moment of self-reflection and unpacking of conservatism/internalized racism that he may have been blind to before, rather than the weird "not all white people" moment that it actually is (though I think this makes hazel's canon discomfort with him even more funny/layered/interesting. like she can smell the internalized bigotry he needs to unpack or something /lh). I also think that reconnecting with thalia would be infinitely more essential to emphasize and show in-text for clear reasons, and that's just not a thing hoo bothers with much (I think that the thalia-jason reunion scene occurring in leo's pov in tlh is like… top 10 worst writing moments in hoo. it so obviously should have occurred in jason's pov and I can't believe rick didn't do that. it's so bad). this is all a pretty big subject that ought to be handled with thought and research and delicacy but I just think there are plenty of reasons why jason specifically being black has potential to be very compelling!!!