I'll be the first to say this is an old poll and I am more than welcome to see new contradictory evidence if it can be presented but....
https://www.cnn.com/2019/03/14/politics/independents-pew
I have never really met a self identified "Independent" who has had a truly centrist position (or; who argues "both sides" with equal vigor)
What do you all think of Independents? IF you are one, do you believe that you are an exception to that rule?
There's two different ways one can be "moderate".
They can either be in the center of the spectrum on most of the issues, or they can hold an eclectic set of viewpoints that average out to around "the middle".
For example, if you asked someone questions from the political compass tests (where the furthest left answer is a -5 and the furthest right answer is a +5)
If a person answers with a -1/+1 on every question
or
A person answers with a -4 on half of the questions, and a +4 on the other half
...both average out to about the same place in aggregate.
Finding someone who's "perfect middle" on everything is going to be nearly impossible.
But with regards to not encountering anyone who argues for/against both sides with equal vigor, that's not exactly an accurate indicator, as you'd have to negatively weight the topic(s) that are getting talked about the most.
Example:
If "Dan Smith" is right-wing on Immigration, but to the left on a myriad of other issues, but Immigration is virtually all that's being discussed on here round the clock, and none of those other issues get discussed regularly, then that's going leave some with the (incomplete/inaccurate) impression of "Well, Dan's just a right-wing person who feigning being a moderate for more credibility and to give his arguments the patina of objectivity"