> What evidence?

Similar evidence to that that does not suggest eating lettuce reduces baldness.

> It's strong relative to the most popular programming languages in use today.

On an expressivity scale, as far as functional correctness is concerned, if Python is 1, Java is 2 and Agda is 100, Haskell would be at maybe 2.5. Sure, stronger, but not enough to suggest it has some real impact, and, indeed, none has so far been found.

Interesting. What are some other languages that would be above 2.5 on your scale?

The jumps in expressivity are not very gradual, and the reason for that is the exact same one as computational expressivity growing "suddenly". PDA's are much more expressive than DFAs, and TM's are drastically more expressive than PDAs.

Liquid Haskell would be a big jump (say, to 20), and anything more than that would put you close to, or at, 100.

But note that type systems are far from the only way of expressing correctness properties. Eve is untyped, but its ability to express correctness properties is much higher than Haskell's. Also, even type systems that are designed for functional correctness do not necessarily do a good job at it compared to other approaches.