The main obstacles to nuclear propulsion seem to be political rather than technical.
I agree, unfortunately the political obstacles are formidable.
Chemical powered booster: really, really, expensive.
This is the reason why nuclear propulsion was discarded. There is unfortunately no compelling (economic) reason for manned space travel, and the specialized robotic missions that NASA and similar agencies mount each cost a lot more than the cost of the expendable boosters used launch them.
If we built such a thing, and sent humans to visit Mars and begin to colonize the Moon, I would be thrilled. But it isn't going to happen in our lifetime.
That's why we can't launch from the US, but any place that is reasonably close to the equator will do. Is Mexico hungry enough?