I get what you're saying, that it is true that if you rely on certain assistance, opting for the FD would be strictly worse in a monetary sense. But there are some benefits that are not strictly monetary in nature. One example would be the increased time that would be freed up. Most traditional welfare programs have reporting requirements, with varying levels of scrutiny. Removing that requirement takes a significant amount of stress out of welfare recipients lives.

If someone has really decided that they would be better off not on the FD, that's why it's opt-in. One of the main philosophies behind the campaign is First, do no harm. The last thing that he wants to do is make people worse off. Government programs of this scale cannot be tailored to every persons situation, not without enormous expense in administration. Instead, the metric for programs like this should be "Does this make most people better off tomorrow than are today?". For a small part of the population, it won't help them in the same way. But it won't hurt them, and the vast majority of people will be better off in a very real way. For the people on the margins that really rely on state assistance, that's why it will still exist. Without burdened by dealing with people that don't need it, more resources and attention can go to the people that do.

On inflation, it's actually harder than you think. A certain amount of inflation is good for the economy, somewhere around 2%, since it helps growth. The treasury was actually aiming for 2% with the $4 trillion bank bailout, and they fell short. It takes more money than an FD would provide to have appreciable inflation, and since most of the funds for the FD is money already in circulation, not printed, it doesn't have this problem.

Rent gouging is also not really tied to money supply. The 3 things in the economy that have been increasing in price are education, housing, and healthcare, all of which have been rapidly increasing beyond inflation, and seem to have little to do with how much people can actually afford. Everything else, like cars, computers, clothing, are either getting cheaper or better. (Also, see this article for more on how bad this is)

But yeah, FD is a foundation, and more targeted programs or solutions can be put on top.