> ...where is the proof that it won't hurt long term productivity, and where is the proof that it doesn't cause inflation[?]

Assuming we could obtain reliable proof that UBI reduces productivity and/or increases inflation, that doesn't necessarily imply that it's an undesirable policy. The economy exists to serve humanity, not to maximize productivity or minimize inflation. It's certainly possible that a policy could provide an overall benefit to humanity while simultaneously reducing economic productivity and/or increasing inflation by some amount.