I'd say it's one of the rare ideas that almost no one supports. The right obviously objects to redistribution. The left prefers inefficient redistribution. It's hard to say there's much tangible opposition on the far left or that opposition causes consideration or that most politicians are taking a serious look. I think you might have just gone 0 for 5.
The right also tends to like freedom of choice, reduced bureaucracy, efficient markets and price discovery, all of which BI does much better than current welfare systems.
This is an obvious strawman. The current inefficient solution is a compromise between the left (who want the government to help the poor) and the right (who don't want the government to help the poor, but can be persuaded if you mix in enough penalties for perceived sin.)
In order to have an efficient solution you need a majority of people voting to agree on what the goal is.
That's not quite true; just they want the main beneficiaries of redistribution to be the bureaucratic class rather than the working class. What you see as inefficiency (in terms of money reaching the end recipients) is in fact, the actual design doing what it was intended to do. Ideally (for them) ALL the money would go on civil servant salaries.