You're right that Stein would have very little support in Congress if she won, but that's not in the realm of possibility, but to say that lower office runs would do better as independents misses some of the peculiarities of the American electoral system:

• Elections in the United States are longer, more burdened with minutiae and uniquely expensive compared to other democracies. Without the organizational support of a 3rd party (mostly libertarian and green parties in the US as others lack numbers and resources), candidates struggle to even get ballot access for lack of money and volunteers getting signatures and clearing regulatory steps
• Speaking of regulatory hurdles, running a presidential candidate every four years in enough states maintains ballot access for down-ticket races

So you're right that independent runs wouldn't have the baggage that comes with third party association, but you're missing that there are very real benefits to that association.

Of course, if we had public campaign financing and rank choice voting, working class voters could unite and not be divided against one another... Almost like it's that way by design 🤷‍♂️