Yes. But even with infinite time there's a limit to how much you can compress the space usage. And that's an interesting property to study.

In addition you can look at how much extra time you actually need: infinite time is a vast overestimate. The new proof gives much more reasonable time bounds.

That is also what is happening here. When you reduce space to sqrt you are increasing time complexity. The interesting part of the result is that you can make this tradeoff for _any_ problem.