Is the phrase "consistently inconsistent" redundant and does it have a single word?

It does smack of redundancy, especially in the context you provided, where the statement is further reinforced by the preceding 'was and remains'.

Logically anything that is inconsistent will be consistently so, since 'inconsistent' covers any behaviour apart from actual consistency. It's like saying that something is consistently chaotic. What is 'inconsistent' chaos? It gets pretty metaphysical pretty quickly.

For that reason, I'd say the best use for the phrase (and probably the reason why many articles use it), is to create humour.

On the other hand, it can also be used (and is likely the intended meaning in the example you cited) to mean that the results of the exercise fluctuate widely, but also in a predictable way. In which case I suppose the usage is valid, but still a little redundant. I'm not aware of a single term that could capture the sentiment, though.

The phrase "consistently inconsistent" is used for emphasis and a touch of humor, or at least more colorful language. It's not really redundant, as something could be "occasionally inconsistent".

In any case, there's nothing wrong with redundancy when it's used for emphasis or to add vibrancy to the language. Redundancy is just bad when it's pointless.

For example: "Joe arrived after the scheduled time and was late." Well duh, of course if he arrived after the scheduled time, he must have been late. That's a pointless redundancy. But, "Joe arrived after the scheduled time and delayed everything." That's not necessarily redundant. For example, others could have decided to go ahead without him when he was late. "Joe is always arriving late and missing appointments." Technically redundant, but it adds emphasis. Sometimes the difference between pointless redundancy and emphatic redundancy is highly subjective.