If you can measure that some are "not random", there ought to be (I would think) some algorithm that captures such combinations and gives them a quantifiable score, which you can then expand towards "less random" combinations. Perhaps you hit a limit at some point, but it seems to me that there should be a mathematical model to represent "badness".
The issue lies when you associated randomness with a uniform distribution. Contrary to popular belief, they are actually not synonymous. For Cryptographically Secure Pseudo-Random Number Generator (CSPRNG), they are subjected to the next-bit test where you cannot predict the next few bits given the first few bits. That requirement is fulfilled by your OS's CSPRNG and thus it qualifies as being sufficiently random.
Now, back to the topic. Sure, you can reject a result where you have 12 consecutive '0's in your key, but that is extraordinarily rare and it would prob never be executed in any code that you write. Hence, there is no good reason for anyone to include test-cases which tests for this. Going by that, the definition of having entropy would then be having the results for which each character has the equal probability of being in each space (ie. non-biased). A counter-example is this:
52431
43521
24312
Against these which are generated with a CSPRNG:
52440
24595
35269
The former has low entropy, even though each character appears exactly once, which means that by normal standards, you would consider each character as having the equal probability to occur at least once. Yet, that is predictable. The second is generated with a CSPRNG, which is random yet there are repeated characters present. That is unpredictable. Given a large enough set, think infinity, each of the values would possibly be uniformly distributed. The mathematical model doesn't exist, there is no telling of how random something is because it is not designed to be predictable. Analysis with any results are often done with something that can be measured and thereby predictable.
There is no need to implement any algorithms to test for this. Your wallet client probably incorporates /dev/random which is a CSPRNG within your OS. random continually collected entropy from the environment and blocks if there isn't any sufficient entropy being collected. In addition, your wallet also seeds using entropy collected from other sources. Hence, trying to evaluate entropy is unnecessary and provides a false sense of security.