If you remove these patterns, you will get a uniform distribution, which violates the assumption of randomness (though the opposite is not necessarily true).
I disagree. Uniform distribution doesn't violates the assumption of randomness, besides, it is still random, for example, if a certain program will distribute 0-9 integers with the same interval (uniform distribution) the numbers that will be distributed will still random, and it will not stop being random, in my opinion.
This randomness topic of yours is a bit tricky if you are going to let it go deeper in your mind.