According to the Supreme Court justices, who heard the medical evidence

"Alfie looks like a normal baby, but the unanimous opinion of the doctors who have examined him and the scans of his brain is that almost all of his brain has been destroyed. No-one knows why. But that it has happened and is continuing to happen cannot be denied. It means that Alfie cannot breathe, or eat, or drink without sophisticated medical treatment. It also means that there is no hope of his ever getting better."

The evidence was that moving him to Italy would make no difference, and might hasten his end. Nothing to do with costs.

https://www.supremecourt.uk/docs/in-the-matter-of-alfie-evans-court-order.pdf