Even if it isn't cheaper, the costs are better to plan around.
We have an entire bureaucracy centered around benefits and making sure if folks have cheated their benefits. I'm sure we'll need some of the bureaucracy still, but it'll mostly be issues receiving their pay instead of having to screen everyone. Fraud will be more limited in scope because there will be fewer ways to commit this sort of fraud (identity theft, not reporting death, and folks inadvertently recieving double payments most commonly).
We'll still need some social programs. UBI simply won't be enough for some folks unless someplace has cheap, affordable healthcare. Otherwise, folks with expensive health needs still need some support. Yes, this will cost some money, but other folks will simply be able to retire and live off the UBI with no intervention. I'm pretty sure this will be cheaper than the current system. This likely goes down or away completely if everyone has healthcare they can afford.
We'll no longer need to maintain things like the SNAP system (food stamps) because this will simply be included in the UBI. You'll no longer have a seperate card to pay for whatever portion of your groceries are included. We can use existing infrastructure for the UBI payments like we already do for other cash benefits.
We could likely have more staighfoward payroll taxes and less paperwork to fill out with those, both on the government side and the employer side. I'm guessing there are other things I haven't looked over. I think overall we'll have fewer employed in this. Now, there will be the cost of the actual money plus distributing it to everyone in the country. This might make up for the savings above, I don't know as I've not done the math.
The point is this: If we can see these sorts of outcomes happening with UBI, then we can realistically estimate the costs and savings of the two systems. It'd take some work and research, sure, but I think it can be done.And for it to come out cheaper.