if programmers are not actually solving similar problems as part of their jobs, sites like codility provide little value over standard IQ tests. all they do is waste the candidate's time and employer's money.
In my opinion programming is about solving programming problems. There are other important parts - like understanding user needs etc - but solving problems is at the core of it. In practice usually these programming problems are easier - but to test how a programmer is proficient in solving them you need to use harder problems or maybe do some programming speed tests (many easy problems).