The use of randomly generated test data seems like a good thing at first glance. Having worked with several teams that have used this concept I generally discourage the practice. Consider a simple method that joins together two strings. A test using random values may look like this.
Harder to Read
While this is a toy example to demonstrate the problem, in more realistic scenarios the lack of literal values harms the readability of the tests. It is worth noting the lack of literals causes more lines of code as anything that has importance needs to be stored in a variable or field. My biggest concern is when assertions start to become complicated or even worse, duplicate production code in order to pass. If we wish to treat tests as examples, this is pretty poor.
Generating a random string seems easy enough. Overtime the edge cases in question start to ramp up. You have whitespace, special characters, new lines, numbers and much more to worry about if you wish to do this properly. The code to actually generate random values is often shared via inheritance or composition, this makes changes tricky and dangerous as you can inadvertently change more than one test when modifying this common code. If the two inputs need to be different then you could potentially generate the same string each time, leading to flaky tests if you're not careful.
The random aspect of these tests can confuse developers. In the example above, there is only ever one value for each variable. In other words this test can run many times locally and pass, but fail when executed elsewhere. There may be a subtle bug that is only found after the code is declared complete. This issue often causes failures in the build, at which developers declare "it's just a random failure" before re-triggering the build because a value may be invalid for a specific scenario.
Date/Times can be Tricky
Date/Times are hard enough as it is. Trying to randomly generate these is not worth the hassle.
My recommendation is to rely on literal values or value objects where possible, these make the test much more readable and act like an example or specification. Additionally their use allows the inline variable refactor to take place, meaning shorter, conciser tests.
Test Cases/Parameterized Tests
If you wish to test similar scenarios in one go then test cases can help. This is usually the case when you cannot name a test easily because the functionality is the same as an existing test.
The assumption that randomly generated tests catch bugs and cover more ground is wrong. If you really do discover a bug after manual testing or on a live system just write a new test exposing that bug and fix it. Thinking you cover more scenarios by using random values is false.
Property Based Testing
I cannot comment on Property Based Testing fully, but this is certainly an interesting area and does not suffer from the issues above. Worth looking into.
This solution certainly violates DRY. There is clear duplication. If this was production code I would remove it, however for tests my stance for a long time has been to allow this duplication to remain. Readability and expressiveness is much more important. There are valid times when duplication between tests is a bad thing. While this simple example doesn't suffer from this problem I will expand on how to keep your tests expressive but DRY in a future post.