I don't think either Meghan or Harry could cope with the forensic and unrelenting US media and press attention any political career would create. Harry in particularly has been vocal about the impact on his mental health of being in a high profile, institutional role that carries public scrutiny, duty and managed protocol.
They clearly already hate what they experienced with the UK press. It would be much much worse in the USA, particularly when the Republican (I assume she would be Democrat) media outlets and organisations start to dig into their personal lives and histories even further. Nothing would be off the table, including their children, families, ex-partners and so on.
I'm not suggesting that either of them have any dark skeletons that we know nothing of, but if there is anything that can be trawled up and used against them, it will be. Thomas Markle and Meghans half siblings, Harry's behaviour in the Army, all that type of stuff will be rehashed continually to discredit them.
I simply can't see either of them opening themselves up further to that type of scrutiny. I mean, it's why they left the UK in the first place, privacy and the need to step away from sense of public ownership of their lives by others.